Would it be possible to change group-name-rewrite config option into a mysql and command based feature?

So instead of changing the config in every server you could easily do:
/lp namerewrite <group> <new name> [context] and it will be stored in mysql.

I'd prefer /lp group <group> setdisplayname <name> [contexts...].

(also not totally sure if I like the idea of having it dependant on contexts though? Should surely be a similar system to weight?)

Hmm. I think contexts are needed. On a prison server, you use default to display the name A and on other servers, you use a name that has to do with the game mode etc.

I don't really see this working if it's similar to the weight system.

Surely you should just be using different groups in that situation?

For instance, on prison you might use prisonrank1 through to prisonrank100, and on survival survivalrank1 --> survivalrank100.

I personally would do this, as opposed to using rank1 --> rank100, with the group shared between both servers.

You're right, contexts aren't good for this. Weights are the better for this.