I doubt they have the memory to spare to store a few thousand extra strings. Those buggers tend to add up to a lot of memory.
Ehh... not quite i'd say. For instance, in a maximum sized galaxy where every single system has two planets (a decent average, i'd say?) with 25 tiles, if every single tile was named with a string that was around 20 characters or so, you would have fifty thousand additional strings, but the entire size would be less than 2.5kb of data (that's a fairly liberal estimate, at 50bytes per string encoding in utf-16). The overhead for storing those strings wouldn't add too much more to that. That would be if every single tile in a galaxy was named, which obviously wont happen.
As far as storage goes, only store the names of the tiles that actually have custom set names (otherwise, no name). AI wont use it, so you wont get any string bloat in the save file either.
I think this would be a neat feature, but almost assuredly is not going to be something the devs will bother with (at least any time soon), as they've got bigger fish to fry, of course.