Based on a WebKit request we added names to dedicated workers in HTML: https://github.com/whatwg/html/pull/2664.
Tests at http://w3c-test.org/workers/name-property.html (and http://w3c-test.org/workers/shared-worker-name-via-options.html for shared workers, although I guess that's not applicable to WebKit).
The actual spec PR was merged a bit prematurely; multiple vendors were on board with the idea, but not everyone got a chance to review the final proposed API shape. So if there are objections please let us know and we can revise the spec or revert it.
Note that we just changed the spec to make it [Replaceable], to avoid compatibility problem Firefox discovered while implementing. The tests are updated to reflect this minor change.
Oops, I opened a new bug for this.
*** This bug has been marked as a duplicate of bug 188779 ***