Introduction First, Name Second
Do you find yourself not listening attentively during an introduction to a new acquaintance? I sure do. And it happens to others when they're introduced to me, especially since I have two one-syllable names.
To help others remember who I am, I've changed my style. Rather than saying "I'm Bill Byrne, glad to meet you, Jenny," I hitch my name to the back. "It's nice to meet you, Jenny. My name is Bill Byrne." It's different and allows more time to get the other party's attention before I say what I really want remembered–my name.