This is when a character or group has a name change between adaptations (for example, Alice Andrews in the books becomes Alice Allen in The Movie and then Annie Adams in The Series). The change can be applied to their first name, last name or both; that also includes super alter egos.
The key to this trope is that between adaptations, the character must clearly be the same. If they are a Suspiciously Similar Substitute or a Composite Character, then this trope does not apply.
This can sometimes be an Enforced Element. Production studios retain a team of lawyers whose job it is to ensure that every name in every work is shared either by many people or by no people in the area that the work is being produced, a process known as "clearance". This is to avoid a lawsuit: if there's exactly one person named Darkness von Gothick, you're just begging for him to sue you for portraying him as a villain. But names that are common in one place and time might be rarer in another, resulting in a name being cleared for use when The Movie was filmed in Hollywood fifty years ago but not when The Series is filmed in Vancouver today.
This is also very common in foreign adaptations, where names are changed to either reflect the local culture or to give the show its own identity. It may also accompany a Race Lift, Adaptational Nationality change, Gender Flip, or Adaptational Gender Identity, with a character's name reflecting their new ethnicity or gender (usually).
This trope only applies when the adaptation is in the same language as the original. When a character's name changes in a translation, that's Dub Name Change. If a character didn't originally have any name then they're Named by the Adaptation. If it's Based on a True Story, see Roman à Clef. If it's to avoid confusion with a more famous character or person that shares the name, it overlaps with Renamed to Avoid Association. If it's the title of the work itself that changes its name, that's Adaptation Title Change.