Trying to Understand What is Trademarkable

NIKE and the swoosh are both trademarked. So that indicates a source, right?
All items with that name and image are associated as being a part of, or coming from that NIKE family (the source).
Am I right in thinking of a trademark being like an umbrella covering a family?


Okay, if NIKE had one shoe called Cool Colleen Trainer. Is that name trademarkable?

Trying to Understand What is Trademarkable