The actress who plays Rose is transgender and, based on a line from Donna in The Giggle, so is Rose. That suggests that Donna didn’t name her Rose, she chose it for herself.
So is it a coincidence? Is there some significance?
It would be interesting if they revisited it.
Sadly it doesn’t look likely unless they started a show for ‘unit’ the company in the other episodes of the specials. Where they could have Donna, Rose and the Doctor fight threats to earth from a modern day stance, sort of like Sarah Jane Adventures.