If you carry other forms of ID with you with all your different names (preferably with photo), I think it could be explainable at the JR ticket counter - but be prepared for some questions, the ticket staff are very thorough!
If you have time, you can return it to your place of purchase and they should be able to issue a replacement for you. If there is no time, then perhaps you could consider preparing a written note in Japanese explaining your situation to present on arrival. - if you purchased from jrpass.com, email us your details and we should be able to arrange something.
Hope this helps!