Sure, Jazmin has right to Grimaldi name because Albert is her biological father. Point is that Tamara thinks that couple nights spent with a famous guy gives her child ,convinced during brief "romance", a claim to his fame and everything that was associated with it. Normally such claim have children whose mother was in longtime relationship with such famous guy, namely they at least for a while formed a family with that guy marriage or cohabitation. Usually, mothers who have out of wedlock children from a very short liaison with a man, give them their own, not father's name.
I also think Tamara rised her daughter convinced she would be one day a princess of Monaco. In series of interviews given by her friend, Bruce Mccormack, it was mentioned many times.