Later on in time if you do good in business, the name will be very valuable to you. A different name that customers will remember when he or she decides to call you or when they hear about it from a customer of yours that is happy with your service.
I do not suggest names that are used all the time like A1, Fast, Quick or most of all "Joe's Lawnservice". Use a name that is a name catcher like Lawn Rangers, Sta Green, GrassMaster. and etc. This will definitely help you be noticed. Remember keep it simple and professional as possible.
You do not want to decide later on in time that you picked the wrong name for your business now that you spent all that time and money getting your name out there. Take your time, this one idea can help you for many years to come.
I used the name "GrassMaster Lawn Service". I talked with family and friends to help me come up with a name. I was helping a friend of mine clean up his lawn (notice I try not to use the word yard) and he noticed how quick I was and what a powerful trimmer I had. My friend said you are like a master at this, this is where the name came from.
Five years later, it was the most talked about Lawn service and largest in my area. I was also one of the most expensive in the area.
I would also suggest that you register your business trade name with your local city government. This way you are the only one in your area that can use this business name. Generally, this can cover a 50 mile area. You really do not want someone else out there competing with your name.