Sometimes I mistakenly say "Dominos, this is... Errr....Hello?" because I mostly only do PC repair on my days off. If I remember correctly, I just say "Hello, how can I help you." I can't say a business name for a few reasons, but mostly because my brothers use the same number for their businesses. My older brother does car repair on the side, my younger brother does plumbing on the side.
(obviously a joke...)
You should answer your phone with something like "Techeroni Computer Services. This is Jim-Bob, can I help you?" But you should have a real business name and the all of the legal stuff done first. The trust will follow.