I've noticed that my parents don't interact much, if at all, with other residents in their care home. I think this is due at least partly to the fact that virtually all the residents are living "in their own little worlds" and hardly seem to notice other people. I wonder if, once they lose the ability to recognise someone, then they actually start not to register their existence. It does seem odd that, for example, my mother sometimes thinks she is in her own home, but makes no mention of all the carers and other residents being there.
Having said that, apparently during the day (when I don't visit) there are group activities which everyone joins in, and so I think over time your mother will probably come to be recognised (quite literally!) and familiar to the other ladies in her home. Mum made quite a good friend in her previous home: they were virtually inseparable during the day, but Mum could never remember her name or even that they shared a room.