I like number 4, it is very original. Think about it, just naming your company "Other", it doesn't include "lawncare" or "landscape" so you aren't worried about your name labeling you as only doing a certain fraction of the industry.
I'm sorry for being a wise ***, I am over tired right now.
As far as "lawn care" vs "lawn service". I'm not sure about in your area, but in many areas, "lawn service" is what many people think of as landscaping, such as mow-n-blow. Where "lawn care" is generally more of the fert and chemical part of the industry.
Why do people not respect us as they do other tradesmen? Because every Tom, Dick, and Harry doesn't think he can be a plumber or electrician!