I have the same problem in the US. I, as the director of the Montana LLC that legally owns the motorhome, had to draft an authorisation for myself as the driver, to cross the border into Mexico.

In Germany we have another vehicle but to get around prohibition on non-EU people registering and insuring a vehicle, the company we bought it off acts as our proxy and registers and insures it in their name. We carry a letter from the company identifying us as the real owners but it is in German and does not show our passport details. Getting into Morocco was a hassle but luckily the sensible customs bloke just pushed the paperwork across to me and suggested I add my name under the company's. In that case the documents had been filled out by the ticket seller in Spain and it was my first border crossing so didn't know the ropes.
Next hiccup was getting into Turkey - same problem but mainly because of language and no passport details on the letter. No way would she budge. Luckily another officer came along who could speak German and English and he smoothed the way.

So I suggest you arrange for some sort of certified letter, preferably including translations of whatever languages are likely to work wherever you are going. Ideally it probably should be a Power of Attorney or equivalent but I imagine something signed by a JP or Clerk of the Court with some fancy stamps would also work as long as both parties and the vehicle are fully described and referenced
We haven't had problems anywhere else in Europe or the Balkans but I guess the german plates are enough even though the owner's and our details don't match. I'd suggest you will strike problems if you go into the 'stans or Russia so it is worth being prepared

(Obviously you could take along your company documents but trouble might be that there is nothing tying it to your documentation and the customs officer needs some non-forgeable document to do that, and the passport works best.

You don't mention which borders, but I guess you have to plan for worst case. In South America they may pick up the discrepancies but they there are many overlanders getting around with technically borrowed vehicles and there you use a PODER to smooth the way. I have the name of the company as my full name so that is what appears on the registration papers and nobody ever noticed the "LLC" on the end so I never needed the PoA anyway.
If you are going places needing a Carnet then there may be further complications that can't be overcome so of course having all paperwork matching is certainly going to be the best solution

__________________
Tony
Click here for Travel Photos & Travel Map