No on in their right minds are giving these names to themselves. It's the HR "we are all a big family" playbook since forever.
I worked for a company called Weblinc, we called each other Weblincers - not because it was some cult, and there wasn't company "we're a big family" messaging, although there were many tightly knit social groups among colleagues that formed over the years and continue to exist outside of work. That said, when we productized the platform we'd built and rebranded as Workarea, no one made some tribalized adoption of that name. I hadn't thought of it much, but Workarean doesn't roll off the tongue, and becomes an unfortunate homonym, particularly in southeast Pennsylvania.
I'm sometimes called a number of things that I also call myself: a Philadelphian, a Pennsylvanian, a musician, and currently, a commercetooler. It's not my entire personality, but I think it's a little sociopathic to think the company of people that you work with does not contribute in some way to your identity.
People actually do call each other Plaids in certain contexts because it's shorter than saying something like "colleagues" (which sounds overly formal), and it's clear that it encompasses the whole company. I've never heard a colleague say that we're a family or anything similar. Google had a bit of self-mythology about "Googlers" but Plaid doesn't really even have that.