I see nothing in the statute, RCW 4.24.130, or the forms (e.g., King County forms) for a name change that require you to present any specific ID; you need to prove your identity and honest intentions to the satisfaction of the court. Presumably you have documents (e.g., school yearbooks, old photo ID's) that can demonstrate that you've been using the same name since childhood, can produce a marriage certificate to show how the name issue arose, can produce a witness or two if needed, can show that your driver's license, academic records, etc., are associated with your SSN, etc., and as such I would expect that you would be able to meet the demands of a court despite the deficiencies of your formal ID.
Did somebody tell you that you need to do more than that? Who, when and where?

