Depends is the answer. How your credentials were used and how your name was used.
Did the person profited by that action.How and when
Other issues that can arise are Invasion of privacy and false advertisement .
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I am not sure that X has any claims against Y.
Y's customers might have claims against Y.
But, if Y is agreeing to provide a specific product to customers, and then actually provides that product, it seems to me that Y does in fact have the skills necessary to provide the product.
Perhaps X has some claim against Y for showing customer's X's work product, but if Y paid X for that work product, Y would probably have the right to use that work product in any way he likes.