The translation should faithfully reflect the source. Explain the name connection through appropriate evidence instead of rewriting the underlying document.
Keep distinct documents distinct
USCIS translation certification concerns completeness, accuracy and competence; it is not permission to correct the original facts.
Treat the registration as the deciding document for the credential test and gather the complete record for it: the certificate, evidence that it is in good standing on the date of application and the regulator’s contact details in case an officer wants to verify it. Typical costs are certified copies from a civil registry, a replacement or confirmation letter from the institution that issued the credential, and certified translation where a document is not in English. A degree conferred under one surname, a provincial registration under another and a passport under a third is not evidence of anything wrong, but it is evidence of nothing at all until the connecting document is in the folder. A degree from outside Canada is acceptable, but it usually needs a credential evaluation showing United States equivalence, and every document not in English requires a complete certified translation. Build a document index around the claimed role: citizenship evidence, the qualification record, the employer's support letter, and any licence that the occupation actually needs.