What happens to my entitlement?

It depends on whether the assumer is a veteran (who can substitute their own entitlement) or a civilian.  If a civilian assumes your mortgage, the portion of your entitlement you used is tied up until the loan is paid off.  

Does it hurt my credit?

No. The loan balance, interest rate, and monthly mortgage payment simply transfer to the new borrower and purchaser of your home. The loan will begin reporting on their credit and will appear as fully paid and closed on yours, leaving you with no further involvement.

Is this legit?

Absolutely! The very first page of every single promissory note on a VA loan states that the loan is assumable. This actually is part of its entailed benefits.