Basically an distribution that is not a rolling release. Its hard to recommend a specific distribution. You could use one of the Ubuntus, a Fedora Atomic variant, Mint, they should be able to run for weeks without issues. Unless you update a system component that requires a restart to take into effect. Why not openSUSE Leap?
I’m personally on EndeavourOS, a rolling release and update often (even the Kernel). My PC is also on for 24h, usually for days, sometime even a week. One trick to avoid some of the restarts is to just logout and login the user. This should be no problem for you and at least some of the components start fresh due to login.
Finding good project names is one of the hardest things. It depends on the project, sometimes its just in front of you with play on words that has some meaning. It could be some historical reason why you name the project, or something out of blue with metaphorical meaning.
I usually think of a few words and then lookup in thesaurus for words with similar meaning, in example for the random word “management”: https://www.wordhippo.com/what-is/another-word-for/management.html Its often fruitless, sometimes not. So its worth trying if you get stuck.