As for the kid's names being very close together in sound, I can give you a personal experience! My name is Kim. My dad's name is Jim. When someone called, we'd often only hear the "-im" sound. From context, it was always extremely obvious which one of us was needed.
The phone rang at 7pm? "-iiiiiiiiim!! The phone is for you! It's Kate!" That was me.
Knock at the door on a Saturday? "-iiiiim! The repairman is here!" That was definitely my Dad.
I can't remember a single time it was an issue. I could often tell by tone who my mom wanted anyway. Ha.
As for your neighbor? I don't think it's fair to not choose a name because of someone who is in your life at that moment but will probably not be there for your entire life. My parents gave up a name they loved for my sister because she was born near the same time as my dad's old friend. He hasn't spoken to this old friend in about thirty years and I think my mom still laments not using the name.