Good idea but the Doctor doesn't forget everything when he regenerates. I don't think that 10's small circle of friends would make that much difference to a 900 year old man - especially as they'd all moved on to other things since he met them.
Not ony that but there was no reason why any of those relationships needed to change - Rose, Mickey, Jack, Sarah Jane and Jackie had all seen him with previous incarnations and all but SJ knew him as Eccles (can't say for certain where River Song is concerned - for all we know she could have known a dozen Doctors that we haven't even seen yet). In fact, there was really only Martha, Donna and Wilf - that were 10's "new" friends. In many ways, Eccles made more friends than DT - and he have a bit of a flirt with a one or two others.
Even without that, we don't know how long the Doctor had had that body. He could have met huge numbers of people and we know that the Doctor rarely speaks of past companions or aquaintances - at least he didn't until he started talking about Rose to everyone within earshot.
Actually, now I've written that, it gives me another idea for the regeneration - that body could have been wearing out already and absorbing the vortex was just the last straw - Rose may have just been younger and more healthy (even in human V Time Lord terms) and therefore less likely to suffer serious damage.