https://www.epo.org/en/service-support/faq/law-practice/list-professional-representatives-entry/passing-eqe-i-have-changed
Since passing the EQE, I have changed my name. What do I need to do?
If your name has changed since you took the European qualifying examination and differs from what appears on your proof of identity, submit appropriate proof (e.g. a certified copy of your marriage certificate). Please submit the appropriate proof in one single file together with your valid passport or identity card.