No. Switching oil brands at an oil change is fine, and mixing different brands of oil to top up is fine too, as long as both match the viscosity and spec your manual lists. Licensed oils are made to be compatible. Brand matters far less than grade and approvals.
A little too much oil in the engine, up to about half a quart, is harmless on most cars. Around a quart or more over, the crankshaft can whip the oil into foam that doesn't lubricate, and the extra pressure can push oil past seals and into the intake. Drain the excess before driving far.
The best oil for a BMW is any full synthetic that carries the exact BMW Longlife approval your engine calls for, not a particular brand. Most US gas BMWs take LL-01 (usually 5W-30 or 0W-40), and B48 and B58 engines from about 2014 onward also accept LL-17 FE+ 0W-20. Check the approval printed on the bottle against your owner's manual.
If your manual says 10,000 miles and you use the specified synthetic, an oil change every 10,000 miles or 12 months is fine for normal driving. Use 5,000 miles or 6 months if you mostly make short trips, tow, idle a lot or drive on dusty roads, which describes more drivers than you'd think. Never go past a year.
Every engine burns a little oil, but a car burning oil fast usually has worn valve seals, worn piston rings, a stuck PCV valve or a leaking turbo seal. Makers accept anywhere from a quart per 750 miles to a quart per 2,000. Keep it topped up, measure the rate over 1,000 miles, then check the cheap causes first.