Re: Why should a girl change her surname after marriage?
Exactly. Your fiance realized that him asking you to change the name is PURELY a emotional thing. There is no religious or legal reason behind it. No logical argument as to why it “needs” to be done. So when your cornered him…he just gave you a BS reason. 
If you don’t have an issue with changing it…then that’s your personal decision. I don’t think there’s anything wrong with women who make that choice out of their free will. But don’t do it b/c you believe there’s a legal reason for it.
P.S. Looks like your fiance has a habit a babbling total BS just to give you the impression that he’s “right”. You may want to keep this trait of his in mind in the future when disagreements happen. Double check FACTS instead of believing things blindly. 