I would have recommended Ace Attorney, Snatcher, and VA-11 Hall-A if you hadn't already named them so that saves me some time.
Fair warning, most of these are going to be far longer (and very different) than DDLC, but here are some of my personal favorites in the visual novel space:
Collapsible section because this is a very long post
Speaking of Ace Attorney, while I think this other series is just decent and nothing really spectacular, if you want something that's a lot like that, the Danganronpa series (minus an action game spinoff) is basically Ace Attorney's gameplay transplanted into a high school setting with a "death game" premise and some light dating sim elements sprinkled in. The overarching narrative is eye-rolling but some of the cases are really good, and I enjoyed the more action-oriented take on the Ace Attorney courtroom scenes where debate occurs in real-time and you need to actually time your responses.
If you like sci-fi thrillers, some of my favorites are the Steins;Gate and the Zero Escape series.
The former is about some college kids who stumble upon the secret of time travel when they invent a device to send text messages back in time (and this later leads them into the depths of an international conspiracy); just make sure to play the original version and not Steins;Gate Elite, which is a recursive adaptation of the anime adaptation and a pretty blatant cash-grab. The non-linear sequel, Steins;Gate 0 (basically it's a what-if story where the events of the first one's true ending go slightly differently) is also really solid. Really my one gripe with S;G is that it completely lets down its transgender character and the second half of her narrative is easily the worst part of the game. Anyway, Steins;Gate is unique for the way you interact with its world: the majority of your interactions comes via the ability to pull up the protagonist's cell phone at any time, and your path is primarily determined by whether or not you answer it when it rings, and when you send and how you respond to text messages.
Zero Escape is a trilogy of games that are essentially a more strange high-concept version of Saw, where a cast of characters are trapped in some dangerous location and need to cooperate and compete with one another in order to escape. In addition to the traditional visual novel gameplay, your reading is also periodically interrupted so you can solve point-and-click escape room segments, the same puzzles that your characters face. In the first two, the narrative branches based on things like which doors you enter and by extension which escape rooms you explore; the third is more experimental and nonlinear. The first ZE game (Nine Hours, Nine Persons, Nine Doors) is the strongest of the three, but the second is also really good, and the third is... fine. Although I do strongly recommend the original Nintendo DS version of 999 (emulate it if you have to) as it was designed around that specific hardware and the narrative really loses something when it's all crunched down into one screen in the later ports. I don't want to spoil it but the short version is there's a late-game plot twist that doesn't have nearly the same impact in the remaster.
AI: The Somnium Files is the current series from the writer behind Zero Escape and it's also quite solid. It's a sci-fi detective thriller that I thoroughly enjoyed despite some admittedly pretty major problems with inconsistent tone. So far it consists of two games: the original and a sequel called NirvanA Initiative. In these, you get similar puzzle segments to what you would see in ZE, but with some new gameplay twists (and more surreal puzzles since they take place inside dreams). They also tend to have multiple solutions, with the plot branching based on which answer you found.
If you're familiar with the games of Goichi "Suda 51" Suda and his company Grasshopper Manufacture (games like Killer7, No More Heroes, Lollipop Chainsaw, Killer Is Dead, or Let It Die), you might enjoy The Silver Case and its sequel The 25th Ward. The former was his first ever game, and it's another detective thriller. Really, mystery/thriller is a far more common genre in the visual novel space than people tend to think, and it suits the format pretty perfectly.
Fate/stay night is one of the most popular VNs of all time for a reason: while the franchise that followed it is mostly garbage (in my opinion), the original visual novel holds up extremely well. It's a modern fantasy story that tackles some really interesting themes, particularly in its latter two routes (there are three, but you're required to complete them in a specific order). The original release contained several pornographic scenes, which were clearly ghostwritten and of a notably lower quality than the rest of the game, but later re-releases (subtitled Realta Nua) removed them and it's a much better product as a result. Unfortunately, there is no official English localization and the PC version of said re-release is no longer sold, but a fan translation that includes several additional improvements exists and can be found with little difficulty (search for "fate stay night realta nua ultimate edition"), and the game itself can still be found via unofficial means if you know what I mean.
The When They Cry series is famously good albeit very, very, very long. It so far consists of three games, released episodically: Higurashi, Umineko, and (the currently ongoing) Ciconia. Higurashi is a horror story, Umineko is more of a murder mystery (and is possibly one of the best VNs ever penned, though it's around 2.5 times as long as War and Peace in terms of word count), and Ciconia is sci-fi.
I've personally rather enjoyed the works of Christine Love (Digital: A Love Story, don't take it personally babe it just ain't your story, Analogue: A Hate Story, and Hate Plus; I have not played Ladykiller in a Bind yet) but her earlier works are definitely on the rough side and Ladykiller is um, adult in nature. Still, Digital and don't take it personally are both very short and available for free.
I haven't played it myself yet, but I hear overwhelmingly positive things about The House in Fata Morgana. It's horror.
And by far the most niche suggestion on this list, which I've been dancing around naming for a while due to this, is Echo (not the shooter, a visual novel that happens to share its name). It's free on itch, and like DDLC it's a cross between dating sim and psychological horror, albeit much more subtle and on much more of a slow burn. And, though I concede the similarities between the two are purely superficial, it's also leagues better than DDLC in every conceivable way. It's about a journalism major going back to his dying childhood hometown over spring break, both to work on a project about the town's history and to meet back up with his childhood friend group one last time. It doesn't go well: old secrets resurface, cracks appear in the group's cohesion, and this is all before the town's supernatural horrors make themselves manifest. Across its five character routes, Echo tells a truly harrowing story, each narrative adding something new to the whole, answering some questions while raising others, and connecting to each other route in subtle ways that you probably won't even notice until you've finished all five and can start making those connections for yourself. In spite of some minor continuity issues with itself resulting from the way it was written (gradually updated and finished over six years), it's all very tightly-plotted and every single route is also really good on their own. TJ's route, for example, is one of the most viscerally uncomfortable things that I've ever played in my life, while the good ending of Leo's route hit me in a way nothing else has and forced me to take a break for a while, Flynn's is a winding mystery with multiple shocking turns, and Jenna's thoroughly engrossed me with its powerful themes and also has one of the most terrifying jump scares I've seen in my life (Carl's is definitely the weakest of the five but it's still better than some entire VNs).
The thing is, the reason I've been so cagey about recommending this one, is that it happens to be extremely gay (the protagonist himself is bisexual and four out of the five routes involve romancing other men) and all of the characters are furries. And there are a couple of sex scenes, which are not skippable. The thing is very clearly geared for a highly specific audience (the overlap in the venn diagram of queer furries and psychological horror fans is unquestionably pretty narrow).
Yeah, it's really not for everyone, but it is also one of the best visual novels that I've ever played (and it's free). Pretty much as soon as I finished it, I started writing about it, and now a month later I'm about halfway through the script for a feature-length video essay on the thing because there is so much to analyze and talk about. I am not going to link to it because off the top of my head I don't know what this forum's policy is regarding adult content, but I will just reiterate that it is extremely good.
I could probably think of a few more if I had the time but this post is already getting way too long.
And if you're curious, my personal top 5 favorite VNs of all time are in fact all on this list. In no particular order: 999, Steins;Gate, Umineko, Fate/stay night, and Echo.
