a big reason i rename my starbases immediately after contructing them. then at least the alphabetical sorting helps me a bit. but the info you mentioned would be a nice addition.
the way sorting works on the mini lists could use a slight tweek IMHO. on the planets mini-list, for example, there are many useful ways you can sort the list, but the sorting option itself would work better as a pull-down list. it can be frustrating using the left/right arrows to cycle through the various options, especially because i don't always remember the name of a particular option, and IIRC they're not in alphabetical order anyway.
I've taken to keeping the number but renaming them by 'sector' for a given region, with a suffix for type - i.e. "Thalan 1032m" for a military base in the Thalan sector, except for resource bases which I get a little more descriptive on since there's so few of them "Science Station Galileo" "Fuel Depot IV" et al.
Renaming is the only way I get good use from waypoints too - I pretty much keep one waypoint with the same name on every Starbase, then switch transport outputs as required, with a couple 'at large' waypoints for things like fleet formation.