Is it weird for an ex wife to keep her ex husbands last name??

So my fiancé’s ex wife has his last name. Should I take his last name when we get married in May? His ex wife also a daughter that took my fiancé’s last name. Her daughter is not my fiancé’s biological daughter and he’s not on the birth certificate. I do have a daughter with my fiancé and she has his last name. I feel weird taking his last name cause of his ex. She also just had a baby with her daughters real father me and my fiancé don’t know if she gave my fiancé’s last name to her son. If she gave her son my fiancé’s last name does that mean she still in love with my fiancé?