ex wants to use my name?

My ex divorced me, remarried and moved from Texas to Florida. Her new marriage has ended in divorce and now she is asking if I have any objection to her changing her name back to mine. She says that since our kids (minors) have my name, it would be more convenient. She also says she doesn't need my permission to do this. I don't really care if she uses my name, but am concerned about future consequences... financial and legal. Appreciate assistance.

what financial and/or legal consequences are you worried about if she takes back her old married name?