Will changing motor oil brands, have an ill effect on my cars engine?

“The instructions are very easy to follow: Simply change the oil as you would normally. Any “confusion” is just myth. You can switch from conventional motor oil to Mobil 1 synthetic (and back again, if you want), without following any special procedures.

The only exception to this is with a higher-mileage engine that has never used synthetic motor oil, or with an engine that has used conventional motor oil and been poorly maintained. In these cases, you should still follow the same basic oil-change procedures (drain the old oil, remove the old oil filter, put in new Mobil 1 and put on a new oil filter), but you should follow a regimen of one or two shortened oil-change intervals. For instance, let’s say that your regular oil change interval is 5,000 miles. If you’re switching to Mobil 1 under the circumstances mentioned above, make your next Mobil 1 oil change in 2,500 miles, your third Mobil 1 oil change 3,500 miles after that, and then follow your normal 5,000 mile oil-change interval. The reasoning behind this staggered interval is that a high-mileage engine, or one that has seen infrequent oil changes, will likely have a considerable build-up of sludge and deposits. Mobil 1 will help clean the engine as you drive, but it will have to work much harder in a very “dirty” engine, and so it is best to change the oil more frequently for those first few thousand miles.”

Source

I have a Jeep Grand Cherokee that I have owed since it was new (8 miles). I have used different oils and brands. I never used a synthetic. I however religiously changed my oil between 3,000–6,000 miles of use.
The last 150,000 miles of life I have been using 1 quart of Lucas Oil Stabilizer due to the high mileage.
The engine (4.0L – V6) has 355,000 original miles and zero issues. Still drive it everyday.

What @marinelife said is pretty much correct. There is no real harm on your engine in switching between synthetics and the regular, in fact in most cases synthetics are a lot better for your engine. The exceptions are, as he pointed out, older cars that were not properly maintained in the first place.

We switched to Mobil One oil for a Caddy with an aluminum engine and it was a very good thing indeed.
The car was stolen a few years later and is still probably running like a top

I do know that on a VW Passat 1.8L with turbo that you need to only and always use synthetic oil or it develops sludge that will kill the motor. I don’t know if this is an issue with any other motor, but since it is with that one, it may be wise to do some research for your specific model.