It's great that you don't want anyone to confuse you with SW/Eden, which previously had the name you now use. But it would not be confusing at all if you selected a name that is original. Having worked in marketing for 20 years, I would never advise someone to recycle a business name once used by a different company in the same field because it looks like you want to benefit from their reputation...Unless that is the goal in the first place.
RE: We are "not" SW/Eden --- Our Social Networks for EOS SWEDEN (Quick Clarification)