how to setup apple watch without old id

Sounds like you do not recognise this other Apple ID? Did you just buy this Watch used? I suspect that the previous owner did not unlock it 

Any Apple device with activation lock still applied is totally useless to the new owner unless the original owner can be contacted. 

If the Apple ID is yours but maybe an old one, then https://al-support.apple.com/#/getsupport

Further information can be found here About Activation Lock on your Apple Watch - Apple Support