That's funny. I decided the same thing this year. I'm not gonna tell you what I changed it to, but I will tell you that my previous name was exactly like yours "my first name's lawn service". This happened because I didn't really intend on it growing as large as it did. I never thought I would make a career out of it.
A helpful hint that drove me to pick my current name is that in order to describe everything I do I had to use a very broad name. It also leaves me with the ability to expand into other services or get rid of services that don't provide enough revenue.
My only other hint is to not use corny cliche names. There are names that we have all heard and seen (i'm too scared to mention any because I don't want to offend). Just because someone isn't using it in your area doesn't mean it's time to go grab up that dba because someone else hasn't.
Wish I could be of more help. I just struggled with this myself. You'll find something that fits.