I am trying to pair my new phone with my watch. I do not have my old phone and do not remember my old Apple ID what should I do?

You can request an Online Activation Lock Removal HERE.

Or this;

If you can't remember/gain access to the apple id that paired the watch to the phone.Take the watch and it's receipt along with some photo id and any other proof of ownership to an Apple Store and request that they remove the Activation Lock for you.

Then;

How to pair your Apple Watch with a new iPhone – Apple Support

Maybe make a new Apple ID or get the old phone.