I'll add again the codenames / project names of the previous coasters for reference:
X:\No Way Out: Project X
Colossus: Project Odyssey (a coaster was meant to open at Thorpe in that site in 2001)
Nemesis Inferno: Project Calypso (it went into the area called Calypso Quay at the time)
Stealth: Project Stealth (the name was ironic, because of the height. It just stuck. It was almost called The Edge. Humdinger was also considered)
Saw: Project Dylan (named after the lead project manager's cat, as something random which couldn't be related to the name, after Stealth)
Swarm: Project LC12, Long Count 12 (because 2012 was end of the world according to the Mayan Calendar)
To expand on these more...
Project X was a generic mysterious sounding name. I believe it was mentioned during the marketing for X:\NWO and on the 1995 park map.
Project Odyssey was a nod to the film 2001: A Space Odyssey. Originally a coaster (a Premier launch I think) was meant to go in Colossus' space. I don't recall it ever being mentioned in marketing.
Project Calypso was because of the name of the area. The name Nemesis Inferno was announced quite early, and I don't think the project name was ever mentioned in marketing.
Project Stealth was meant to be ironic. It was meant to end up being called 'The Edge'. The sign was printed and put up, and even some merchandise with the name was made. The long-standing rumour is that at the same time, Pizza Hut UK had trademarked the name for a new pizza they were advertising, hence the last minute name change. Stealth was chosen because it simply was referred to by a lot of people as Stealth.
I've never heard of confirmation either way whether the pizza rumour is true. From a personal standpoint I'm a bit dubious about it, as I:
1. Would have thought that Thorpe would have been trademarked the name before Pizza Hut
2. The trademarks would have been different.
As mentioned, another name under consideration before The Edge was chosen was Humdinger.
The project name was mentioned in marketing, as the park set up a mini site for the construction and marketing.
Project Dylan comes from one of the project manager's cats, who was named Dylan. They wanted to do something completely random, partially as a result of the Stealth naming. I can't remember if it was mentioned during marketing, but there was a mini site for construction, so probably was used there at one point.
LC12 was, as said, in reference to the Long Count calendar, with the usual story of the world ending in 2012. This was pushed a lot more during marketing and teasing for the ride, which was very fan-focused.
In more recent years, it's been more common for more people to know of codenames and for the park to use them. Wicker Man's teasers had SW8 references a lot for example. It's also common for parks, especially Thorpe, to play up to goons and geeks a lot more.
Whilst I'm here, I'll rattle off some more Thorpe project names I can remember:
-Derren Brown's Ghost Train:
WC16. WC stood for Whitechapel, which I guess was a hint to the Victorian stuff, and 16 for the opening year.
-Storm Surge:
Oily Rag. No clue.
-Angry Birds Land:
TV4D. TV stood for Time Voyagers, the park's previous 4D film, which the area replaced.
-The Walking Dead: Living Nightmare (Fright Nights maze):
Project Baseball. A nod to the baseball bat related to the character Negan.
-The Walking Dead: The Ride:
Project Evolution. I dunno, evolving the ride I guess?
So really, the project name could mean anything at this point. Exodus could have some relevance to the theme or story, it could be the name, or it could be completely unrelated. The park probably have some reason for it, but we won't know it for a good couple of years I reckon.
It's probably too soon to read into whether the Exodus poster in the Trailers maze is giving us a hint to the theme. My personal opinion at this stage is that it was more a reference to the location, given the background was similar to the trees in Old Town.