How to put Signature in iMessages/sms

You cannot, iMessage is like any other instant messaging app, you always know who you are talking to and there is no need for a signature: the recipient also knows whom the message comes from.

It is not possible to do with the iPhone. Some users have created a Text Replacement that will enter a specific phrase when you type in a specific shortcut. If you go to Settings>General>Keyboards, then you will see Text Replacement. You could type in YourSignature as the phrase, and then a shortcut that will expand to YourSignature when you complete typing.