Your paycheck can have the name on your license. The problem is the name on your W-2 and your tax returns. The name on those documents should match the name on your Social Security card. Otherwise you may not be getting the correct credit for your earnings for Social Security purposes. You should be able to contact your local Social Security office to get your name on your Social Security account changed to your legal name. If you have been filing tax returns on paper (instead of electronically) using your legal name, the IRS may have been fixing the paper return rather than contacting you. If you have been filing electronically, the return should have been rejected unless you use the name on your Social Security card for filing the tax return.
One other possibility is that you did change the name on your Social Security account to you legal name, but, for some reason you are not using your new Social Security card. In any case, contact Social Security and make sure you are getting credit for all your earnings and that your information with them is up to date.