From a purely technical point of view, short names don't hurt. They don't help either. A shorter DB name won't make backups run faster, queries run faster or decrease the load on your CPU or network.

So, from there, it becomes strictly a question of opinion. Does it make more sense to make typing a connection string (which usually isn't typed very often, at all) easier or should you go for clarity. I think most people here, and elsewhere, will fall on the side of clarity. But it's just an opinion.