If I did not sign a quit claim deed that was gifted, but my name is on the deed, give me the same rights as the primary? (who DID sign)

A person who receives property by quit claim deed (the buyer) does not need to sign it. Only the person giving the property (the seller) needs to sign the deed. It doesn't matter if the property was sold or gifted--the terms buyer and seller still apply.

If your name appears as the buyer on the deed then you have the same rights as any other buyer listed on the deed.