The Stone Mountain Titan mentioned in Godzilla: King of the Monsters is Tiamat. Tiamat is just one of several Titans confirmed to exist in Legendary's MonsterVerse, but never seen. Godzilla: King of the Monsters never reveals what Tiamat actually is in the MonsterVerse, but as is the case with the movie's other missing Titans, the creature's mythological connections could hint at its true nature.
Godzilla: King of the Monsters greatly expands on the third M.U.T.O - appear in the flesh during the events of the movie and are on hand following Godzilla's victory over the "False King", Ghidorah. All the other Titans are kept hidden, but a monitor screen at one of Monarch's bases reveals their names and locations.
One Titan in particular is directly referenced following King Ghidorah's call when it's stated that the Titan secured at Stone Mountain has escaped. Stone Mountain, Georgia is the location of Monarch Outpost 53, which according to Monarch's map, is where Tiamat was being monitored. So who is this Tiamat? In popular culture, Tiamat is generally depicted as a multi-headed, fire-breathing dragon, thanks to Dungeons & Dragons, but this isn't always the way Tiamat has been viewed. Tiamat has her origins in Akkadian mythology.
In ancient Babylon, Tiamat was regarded as the goddess of the ocean and is given shared credit for creating the Earth. Tiamat was sometimes thought of as humanoid in appearance, but has also been described as a sea serpent or female dragon. However, this description is disputed by some historians, and it's hard to say exactly how Tiamat was viewed by the ancient people of Babylon, or when she started being associated with dragons.
What the myths say about the MonsterVerse character is that the Titan could in fact be yet another dragon, which the MonsterVerse may already have in abundance. King Ghidorah is dead, but other possible dragons in Legendary's cinematic universe include Godzilla vs. Kong.