Taking An Existing Program And Re-Branding It?

What are your thoughts on this as a business move, for example, i know when TopBucks first started they used the name TopCash, which they eventually switched out to their mainstream offerings (and subsequently closed a few years later) im actually in a similar situation right now as i have a business opportunity that has arisen that i could use an existing program of mine for but it would mean having to migrate 4 sites over to a new program name instead.

Do you think something like this would work well given the state of the industry these days or do you think it is better to leave things how they are and start a new program for the new opportunity?

Your thoughts please?

Regards,

Lee