Could Ilmor come back as an engine (re)brand (although I cant remember it ever being used as part of a team name)?
Ilmor *as it was* is now named Mercedes Benz High Performance Engines and is fully owned by Merc. They currently make all the Mercedes F1 engines.
But Ilmor does exist again now as an entirely seperate company. Makes all sorts of high performance engines for various uses, racing, military, boats and so on.
And for the last part:
Tyrrell, Leyton House (renamed to March the next year, same engines), Sauber, and Pacific all ran Ilmore engines and were named as such.
*off to the geek corner*