Microsoft Mini-redirector (which is used by Windows Explorer to access the WebDAV server behind the scenes) ignores display name returned by WebDAV server and just uses the last part of Url as a file or folder name.
The only way to achieve identical behavior in Windows Explorer and other WebDAV clients is to return the same text both for folder name and for Url part. That is in your case, to make names human-readable and identical to what Ajax File Browser displays, your Path implementation must return ‘/Folder/My Folder/’.