If it's listed in the yellow pages under tree service, people will find it. If it's on your equipment and they see it while you're working on a job, it's obvious what you do.
Sometimes it's good to have a name that isn't so descriptive. When people ask about your company, you have an open door to do a vocal sales job which can be far more impressive and memorable than any clever name that basically says you cut down trees and haul them away. Be sure to stress your safety record and quality of equipment as well as experience and qualifications.