In Japan your first name is your family name, your last name is your personal name. I never know what people mean when they ask me what my last name is here in Japan.
My full name is Kathleen McGregor, which is an absolute nightmare for Japanese people to say. In fact my name is unfortunately difficult for most non-English speaking people.
When I introduce myself in America I say. "My name is Kathleen McGregor, but please call me Katie." This does not work in Japan. The idea of immediately asking someone to call you by a nickname seems overly casual for a first meeting, which makes many people uncomfortable. So, here in Japan I say ( in japanese) "I'm McGregor, Katie". I then wait for them to look at me absolutely terrified at the idea of trying to say my name, at which point I say ( in Japanese) "Ms. Katie, if you please."
For any one interested in what Kathleen McGregor sounds like in Japanese here is my name in romaji ( notice the number of syllables): Kasurin Makuguregaru.