Girlfriend = "grandma"

ArcticFox

We had my FIL and his girlfriend over for a BBQ on July 4th.

FIL has been going out with her a couple years (2-3? I don't even know because he never brought it up until DH randomly met her).  She has been invited over plenty of times, but the first time we met her was in March for DD's bday party.  I know she bought a lot of gifts for the kids over the years, because FIL would come over with nice stuff, which is totally not something he does.  I feel like she's tried to be involved, but I've only met her for about 1 hr at DD's party and about 3 hours at the BBQ.

Anyway like an hour into the BBQ she says to DD and I, that DD can call her "Grandma".  I can understand her wanting to be a part of our lives, but I thought it was maybe a little early for that.  I can see her point of view, probably hearing stories and seeing pics of the kids for several years and not being included, but making a really nice effort.  It's hard to explain, but my FIL makes little to no effort to be a grandparent, and he even goes out of his way to avoid things (like never having the gf over, or saying he's coming to DD's party but showing up 5 minutes after the party ends to avoid any social interaction.

Thoughts? Would you be comfortable with your kids calling someone grandma that they spent only a couple hours with?  This is all new to me, we have been very welcoming to the gf, she just hasn't been a part of things until just now.