If the following happends:
Who will be registerd as the author of that changeset?
TFS creates a changeset every time you do a check in.
All the included file changes from your workspace along with the comment, check-in notes, and links to related work items are stored on the server as a single changeset on your server.
Changeset owner/user is just the one who check files into TFS.
So in your case, it should be person Y registerd as the author of that changeset