Is there any api to get all changed file names in a merge request?

GET /projects/:id/merge_requests/:merge_request_iid/changes gives you all changes, see Merge requests API | GitLab

Or using git:

My Job:
  script:
    - git fetch origin $CI_MERGE_REQUEST_TARGET_BRANCH_NAME
    - git diff-tree --name-only -r "HEAD..origin/$CI_MERGE_REQUEST_TARGET_BRANCH_NAME"