My name is very uncommon among women in my generation but was very common for women in my grandmother's generation so when I used to work in a drugstore when I was in my late teens, I met many 60-something women who would say, hey my name is Martha, too (not my real name). A friend of mine also had a friend whose name happened to be Martha who was our generation. Unfortunately, Martha was a petty thief so it really was better not to have people think I was her. She was also gay so when my friend would mention Martha or he would introduce me to friends who heard of the other Martha, he would immediately self-correct with, "No, you're talking about the gay Martha; this one's straight" (often, they'd ask when we'd be introduced, "Is she the gay Martha" so my friend would say, "No, this is the straight Martha"). I'd never mind being mixed up with her for the fact that she was gay, but I certainly didn't want to be thought of as some petty thief who'd been in trouble with the law a few times!
Also, my DF and my older cat share the same name. When I met DF, he introduced himself by the shortened form of his name, like Mike. Well, when I'd go home, I'd be talking to him and saying hello to my cat, Mike so DF would tease me about whatever I was saying to my cat. I finally started calling DF Michael in order to differentiate between the two (I'm the ONLY one who calls him Michael; everyone else either calls him his childhood family nickname, Mick, or Mike). I call my cat MikeCat though.