You can get something close to that with the TiddlerAliasPlugin (http://tiddlywiki.abego-software.de/Beta.html#TiddlerAliasPlugin), while only requiring a very small manual change. Namely you have to enter as an "Alias" the old title of the tiddler at the same time you change it. This will preserve all link functionality, but it will break tracking of backlinks through the "References" link.
To do otherwise (I am not a developer, only a TiddlyWiki user) would seemingly require some sort of search/replace within all tiddlers when renaming, and I don't think that's possible (I dunno about restoring backlink tracks with something like the MediaWiki redirect system though). It is possible to do that sort of search-and-replace within a tiddler's metadata, though: a plugin exists to rename tags, and will change them on all tagged tiddlers.