The costume save function was working last time I used it. You could load the costumes type in a name in the last screen and then save them. As far as renaming them outside of the costume creator there was a program a player made to do so but I'm not sure if it's been updated since they fixed the in game saves.
Comments
I organize my costume files by name this way. For example I have a file named '01 Dynamo Lass 01' or '00 Unknown' or '02 Meteor Maiden Nem02' etc etc.
00 = Costume file/idea, not currently playing
01, 02, etc = first (main) character, second character, etc.
The name is self-explanatary
Then the trailing numbers are for individual costumes or nemeses.
00 Unknown 01 (character idea/WIP 1)
00 Unknown 02 (character idea/WIP 2)
01 Dynamo Lass 01 (costume 1)
01 Dynamo Lass 02 (costume 2)
01 Dynamo Lass 03 (costume 3)
01 Dynamo Lass Nem01 (nemesis 1)
01 Dynamo Lass Nem02 (nemesis 2)
etc etc