Renting from kingdom strollers. It asks what we want the name tag to say. Do most people put the "smith" family or not want their last names on there so something else?
I put our child's first name (with Orlando Strollers), but DH didn't know and there was a bit of a snafu - Guest Services had a stroller for The Lucas Family (his first name) and it took a bit to straighten out. It wasn't a big deal and we laughed about it, but just remember what name you put it under . I would use our last name if I rented again. It's not a big deal - I don't think I've ever even noticed names on strollers. It's just for delivery and so you don't take the wrong one back to the hotel.
You could put your child's fave character's name if you don't want to use your own. Typically though, it looks like most people are using their last names.