I did an adult adoption last year, my last name changed. Does my W2's and other tax forms have to show new name?

No.  Your W2 and other forms do not have to match your name, as long as it has the correct SSN on it you are ok.  You can enter your new name on your 1040 and that will be fine as long as you updated the social security administration with your new name.  The IRS does match that database.