My brother's girlfriend did this - part 2 ... Why & what would you do?

Maybe they think it goes well with Kaylee and are just using it with no connection to your grandma. Who named the dog, your brother or his girlfriend. Either way, you said he wasnt close to your grandma so I would just let it be. If he actually had a child and names it Jaylynn Mae, then I think I would question his reasoning.