Taking on a second business (Partnership)

System

Help please. I am a Partner in an automobile business (not Litd) and about to invest in another new one. Let's call them "Business A" and "Business B" respectively.
We don't like the existing name of Business B but it doesn't make sense to change the name of a successful business until we are established owners of it. We therefore have to trade under the existing name from our customer and supplier perspective, but want it to be either under the umbrella or part of Business A in some easily accounted way. For example "Business A trading as Business B" or "Business B, a Business A company". And would we have to become Limited? Is it easier just to run the two seperately? Ahhhhhhh! Suggestions on options/the best way forward would be appreciated please? Thank you.