You face two problems here.
- w:c:sherlock has been around since 11 February 2007 — well before Moffat and Gatiss even began work on their version
- w:c:sherlock is about the entire mythos, and you're wanting the prime name — Sherlock — for something that totals a mere 9 hours of television at present. Clearly, the wiki with the broader focus deserves the simplest name.
I personally think you should be looking for ways to merge your two wikis. Wikia should have a "one stop shop" for all things Sherlock Holmes. The front page of w:c:sherlock would appear to be violating the spirit of that wiki, in that it's so heavily focussed on a movie no longer in theatres.
Perhaps if you edited w:c:sherlock for a while, you could petition for adminship, and then bring over the material from w:c:bbc-sherlock.
The problem I have with your current URL is that it's ambiguous. The phrase "BBC Sherlock" means many things — not only the Cumberbatch series, but also the 1951 series, the 1965 series, the 2007 Sherlock Holmes and the Baker Street Irregulars, as well as Tom Baker's Sherlock from the early 1980s.
The other thing is that many non-Britons won't know that the most famous TV Sherlock, namely Jeremy Brett's The Adventures of Sherlock Holmes, isn't a BBC production. Americans are used to seeing it commercial-free on PBS, so they'll just assume it's a BBC thing, when in fact it's ITV.
So for me the url w:c:bbc-sherlock is highly problematic. If I were you, I'd just edit the heck out of w:c:sherlock, turn it into a much stronger and more diverse site than it currently is, adopt it, and abandon the poorly-named w:c:bbc-sherlock.
Once you get adminship at both places, then it's a very simple matter to just export the pages from bbc-sherlock and import them to sherlock.