Usually a certified marriage certificate, divorce judgment or change-of-name certificate from the civil registry that recorded the change. Where several changes occurred, the file needs each one in sequence so no step between the birth record and the current passport is missing.
Assemble the chain in order
Lay the documents out from the earliest name to the current one and check that each certificate names both the previous and the new form. A gap in the middle is what prompts questions, not the number of changes. Keep the certified copies together with the credential documents rather than in a separate folder, so the connection is visible without anyone having to ask for it.
Order of arrival is not order of events. Registry copies frequently reach an applicant out of sequence, and a folder assembled in the order things turned up conceals the very continuity it exists to show. Rearrange them by effective date once everything is in hand, and record that date on a cover sheet beside the document that proves it.
Where one certificate is still outstanding, note which link is missing and what has been requested, so a reviewer sees a chain with one pending item rather than an unexplained jump. A certificate held by a registry in another country can take considerably longer than a domestic one, which is a reason to identify it early rather than to leave it last.