I... can't actually find any game on Steam which is just called "Leviathan". Or any game which could reasonably be called "Leviathan" that bears any resemblance to Dreadnought. Got a linky to share?
The Old City: Leviathan could reasonably be called "Leviathan" for short. It's a first-person exploration game which isn't anything remotely like Dreadnought in the first place. I'm inclined to think it's not what you meant, since you probably wouldn't have found it and bought it if you were looking for an experience like Dreadnought.
Leviathan: The Cargo is the newest game I could find on Steam with the title "Leviathan". It looks more like an interactive visual novel or a point-and-click adventure game than anything remotely resembling Dreadnought. Once again, seems unlikely to be a game you'd find and buy if you want
Leviathan Starblade isn't just "Leviathan" or even "Leviathan: subtitle" but I guess it's close, and newer than The Cargo. It's a vertical scrolling 2D shoot-em-up game. It does at least involve spacehips, but once again, I can't see any real comparison to Dreadnought.
This is the only other game I could find that's actually reasonable to call "Leviathan". It's also the only game I own with that word in the title. It's a really good game, and a lot of fun. It's about custom-building ships and sending them into battle. But, once again, nothing like Dreadnought. it's actual naval battles in water, not flying in the sky or space. It's also a top-down simultaneous turn based strategy game. And the "Jazzy" trailer series they made for the game are pretty epic - but for very different reasons from the old but awesome Dreadnought trailer.
None of those games has any relation at all to Dreadnought, but I couldn't find any game which it would be reasonable to call "Leviathan" which looks, sounds or seems to be competing with Dreadnought in any way.
If you're specifically talking about games with a pricetag and vaguely Dreadnought-ish concept of flying big spaceships around and shooting other big spaceships, there are two single-player games I could point to. Starpoint Gemini Warlords and Rebel Galaxy. You'll notice that neither of these games has "Leviathan" anywhere in the title.
The closest comparisons to Dreadnought in terms of games you can find on Steam are Fractured Space and Galactic Junk League. Both are free-to-play games about flying around in space in capital ships and shooting other people who are also flying around in capital ships.
Fractured Space, for a long time, was being referred to by many people as a "bad ripoff of Dreadnought" after the Dreadnought trailer and some alpha gameplay footage had been shown. Fractured Space went public first though, and the devs have been VERY consistent about listening to the fans. In the meantime, when Dreadnought finally did open up to the public, they botched things horribly right before going into "open beta but we're pretending it's not" and have since actually entered open beta without fixing the core issues. The game was absolutely and almost inarguably at its best in the early stages of the closed beta, with the "progression 2.0" release being essentially the killing blow for the game before they opened it to the public. Since Dreadnought's open beta began, I've been hearing it described as a "bad ripoff of Fractured Space" more often than the reverse used to happen.
The two games have a similar gameplay perspective. Both games involve teams of players in large capital-scale spaceships. Fractured Space takes more of a MOBA-like approach, with each team defending a base as an objective, and with a range of lesser objectives spread throughout each map.
Galactic Junk League is best described as a mashup of Dreadnought and the early days of Robocraft. It has custom-buildable ships with a "core" piece that functions sort of like the "seat" that Robocraft used to have. Ships are destructible on a piece-by-piece basis. The core gameplay is basically the same as Dreadnought - team deathmatch battles with players charging in and slaughtering one another. It lacks any kind of healers, however (also a throwback to the early days of Robocraft).
Overall, both FS and GJL are great games worth playing, and each has its own distinctive features that makes it obviously different from Dreadnought - some good and some bad in each, but since they, like Dreadnought, are free-to-play, it's worth trying them out as well and seeing which of these three games really suits you the best.