You are not overreacting. She shouldn't be calling you names. Of course, we don't know how she's saying it when she does... but even name calling in a "playful" manner can be hurtful.

I agree that you have every right to be angry. I would try asking her to stop.

ETA: You and I seem to have posted back to back. I'm sorry that it doesn't seem to work when you ask her to stop.