Changing password actually depends on the type of wallet you are using, some wallet require some verification via sms or Gmail before you are being able to change your password and no one will be interested in wasting time doing all that.
It does not depend on the type of wallet if it is a noncustodial wallet. Only centralized platforms can do that and they are completely different from noncustodial wallet.
After generating the same password, will the new wallet have the same address as the original wallet?
Can you explain this very well, like it is not relating to what hosseinimr93 posted. If you have your seed phrase, you do not need your password to spend your coins, all you have to do is to create another wallet and set another password.