The dinosaurs name should be george what is the possessive noun?

There is no possessive noun in the example sentence.

A possessive noun is indicated by an apostrophe s ('s) or just and apostrophe (') added to the end of the noun.

The noun "dinosaurs" is the plural form of the noun "dinosaur'

The sentence with the correct possessive form is:

The dinosaur's name should be George.

Note: The noun "George" is a proper noun, a name for the dinosaur. A proper noun is always capitalized.