When can you change a monster's position?
Is that correct?


Yes, it is correct.

Unless otherwise specified or restricted, you can do that what you describe.

You can't, however do so on the turn you Summon a monster, as once you place it on certain position then it has to remain that way until you can legally change it again (either by card effect or rulebook effect). Think of it as the "summoning sickness" that MTG creatures have, just that it applies to position instead of attack permission.

Also, some cards may prevent you from doing so. Examples are Level Limit - Area B, or well any Cloudian Archetype monsters, which can't be placed on defense position or they are destroyed.