I just consistently mention it because it's a huge topic atm and it's to everyone's benefit to clarify. If I'm over here talking about how I'm SO glad I can mute instances willy-nilly as I please but don't mention I'm doing that from kbin, that's going to send a lot of frustrated lemmings scrambling through their settings.
Generic is "(the) fedi/fediverse." But where I'm specifically from may carry connotations in UI or culture for those here, and those not here would maybe prefer a platform name they can actually look up, as has already happened to me once.
I do think the "Blaaah, we got X amount of users and we're the biggest in the fedi!" posts are borderline odd, because yeah, we're not going head to head anymore. The tribalism we've had drilled into us for decades, we have no need of now and I don't wanna see any of the platform politics that's always been in the past. Thankfully, it seems to be stemming from genuine enjoyment instead of elitist gloating, and it keeps itself to a minimum.