Introducing yourself, hand shake?

Is handshake social awkward to a girl you just met? How would you introduce your self after breaking the ice with a girl? Would you just say "Btw, my name is Ali. If you don't mind telling me, what's your name?" with just a smile or would you stick out your hand and say "My name is Ali." to see if they will reach out, shake your hand, and then tell you their name. I believe that a hand shake is really powerful tool. It breaks the physical touch barrier - to a degree. Also, depending on the way you shake the girl's/guy's hand, it shows confidence and leadership. If you don't use any of these methods, what would you do inform the girl about your name in the conversation?
Introducing yourself, hand shake?
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