Does changing behaviour really exist?

I have a dilemma.

Let’s suppose in a couple is some disagreement about a random behaviour. If that person tries to change his behaviour for you, it’s healthy or not?

After a heated argument, you start to see some real change. What if, for not upsetting you, hides it very well and deep inside is the same person as before? And you, knowing it, would you ask him to be himself, or to be how you like?

Does change really exists, or is it just agreement to make things good for both sides?