Set the color profile of my external monitor
How do you know which one is correct?

The answer is, you don't.
You can't unless you have an external reference.

The only way to ensure colour accuracy is to use a hardware colorimeter.
Entry level start at maybe 50 $£€ though a good one will be closer to 200, or more.
If you are making imagery that others will see, then knowing it was right when it left your machine is vital.