As former CMO of Expedia I can tell you that being focused will trump any theoretical upside of having different names. To this day there's a struggle to build daylight in meaning between Hotels.com and Expedia's core hotel business - and there have literally been billions spent on trying to do that over the years. Get clear on who you're for, the problem you solve, what insight you are building against and your positioning against that. There's enough work there on its' own - believe me. Good luck.