Here, loggers are called loggers. Arborists (the ones with degrees and certifications) are called arborists. People who cut trees in tree service type situations are called tree service guys/ladies or tree trimmers, albeit with the understanding often only a stump is left after "trimming". Lumberjack would work, just don't hear it often. I've read that people fell trees but don't believe I've ever heard someone actually verbalize, "I felled a tree this weekend". I've heard many people say, "I/we dropped a tree yesterday". Perhaps more accurately, "We'un's drop tree yestiddy." (That must be said quickly for proper effect.) That's probably totally incorrect from a proper use of English perspective, which is in keeping with much of the vernacular here.
Calling a person who cuts trees a feller or faller, in this area (and this area only), makes it sound like you luncheon with Grey Poupon and kippers washed down with a wine cooler, which is fine if you're into that. Or maybe I just hang out with the wrong people (very likely).
oh you meant the dog. Yeah she’s cute too. She actually does have a kill switch. 
