By such a definition any tradition related to gender would be sexist. The tradition is that the wife will change her name. This tradition is why it makes up the majority of cases.
Not really - this “tradition” as you call it obviously started back in the day when women did not have equal rights in society and only the husband’s lineage mattered.
No, any tradition that favors one gender over the other is sexist. Which is absolutely the case with the tradition of women taking their husband's family name when they get married.