My children are 7 amd 5 now with a step sister who has my husband last name. They all go to the same school so when the other children tease them about not being "real" Brothers and Sisters its hurts their feelings. The only reason the idea was brought up was because my daughter asked for it. As for their biological father, my son remembers nothing of him and my daughter only remembers finding his body after he hung himself. While i do make sure they know who he was and some of the nicer things about him, no i do not push them to remember, it brings up to many questions.
Changing their name won't make them 'real' brothers and sisters. If the kids want to pick on them, they will.
You'll be doing your kids a much bigger favor in the long run by teaching them to have the self esteem to ignore stupid taunts.
(Oh, and btw, I doubt very much that that would be going on without some instigation. Kids in school today deal with kids who have stepparents all the time. In my daughter's school, there is no discernible difference between the way kids with 'real' families and stepfamilies are treated. If they started picking on kids who have divorce somewhere in the family or something non-traditional, EVERY kid would have to be ostracized for some reason or another.)