In the Google Fonts Glyphsets Ismall is called icapitalsmall. There is also an uppercase version called Icapitalsmall which has the same name in Glyphs.
When I try to rename Ismall to icapitalsmall to be consistent with the Google specification, Glyphs replaces Icapitalsmall with icapitalsmall for some reason.
I personally find the naming icapitalsmall/Icapitalsmall more logical and consistent than Ismall/Icapitalsmall. If you think so too, would it be possible to rename it in the Glyphs database?
If not, is it possible to change the name in my personal Glyphs installation?
You mean that when you rename Ismall to icapitalsmall, the app auto-changes the other one so that both glyphs have the same pretty name? That should not be possible – pretty names must be unique across the font, and if you try to give two glyphs the same name, the app will complain and tell you you can’t.
I don’t have an informed opinion on this. Intuitively, the naming scheme used in the Google Fonts glyph set makes more sense to me, but I don’t know the reasoning behind the naming implemented in Glyphs. This presupposes these really constitute a case-folding pair with lowercase and uppercase variants.