6 years ago I got estimates to have a tree removed and went with a company with that name. Great price, friendly guy. I have used the tree service now 3x for other things... and have recommended them. It is a very easy name to remember, their font was in dark green and the F was out of tree branches. I can't remember the plumbers I've used, the fence people, or other contractors... but Forrest Tree Service is very easy to remember!
A good professional tree company name would be Evergreen Plantation Company. Such a name would indicate some live in some extend and then you would have a logo of a plant. Another good name would be The Tree Company. You need to fins a name that gives the theme of the business to the people.