That was no simple slip-up. You don’t just make a mistake like that, not after having to identify yourself like that for the better part of your life.
You actually see her being taken aback by Yellow Diamond’s response. She’s caught off guard, disappointed. She’d forgotten that just “Peridot” wasn’t enough to tell her apart. She’d become used to the idea of being unique.
When do you think that happened? When did she stop seeing herself as “Facet-2F5L, Cut-5XG” and start being Peridot with a capital P? Was it after being stranded, due to the lack of contact with another peridot for months on end? Or was it after the truce with the Crystal Gems, brought on by them addressing her as just Peridot day after day?
Facet-2F5L, Cut-5XG. That’s all she’ll ever be to Homeworld. That’s all all the other peridots will ever be. But on Earth, she is Peridot. The one and only. In a way, that’s gotta be liberating.