This link is the 200'+ prominence list of peaks; you'll see quickly that if you raise the bar to 300', two of them drop off. This gives a list of either 17 or 19 13ers in Utah, depending on how strict you are about counting unique peaks. I've heard that you can even stretch the list to 21, although I'm not sure how or what list does so.
For the most part, you'd think that that such prominent landmarks would be named, but as you can see from the list linked above, most of them are not. On any list, only 8 Utah 13ers, all in the Uintas, have official names. The rest of the peaks have unofficial names either taken from the USGS benchmarks on the summits, or from guidebooks where some author gave the peak a name, or just from some nearby geological feature like a pass or a lake that does have a name.
The named 13ers are, in order:
- King's Peak 13,528
- South Kings Peak 13,512 (it barely squeaks out as under King's--then again, until the '60s, this was actually believed to be the highest peak in Utah)
- Gilbert Peak 13,442
- Mount Emmons 13,440
- Mount Lovenia 13,219
- Tokewanna Peak 13,165
- Mount Powell 13,159
- Wilson Peak 13,060
Five of these cluster around the King's Peak area, a 6th is on the nearby Red Castle area, and Tokewanna and Lovenia are just a little bit to the west. Even if you add the un-named 13ers to the list, that pattern holds; the 13ers are all in a narrow band between the Tokewanna ridge cluster to southern the end of the King's-Emmons ridge. All of the peaks to the west of this group are under 13,000 feet (although thy are often more scenic and dramatic in other ways; check out Mount Beulah or The Cathedral for rugged, scenic views, for instance.)
For an image, here's a view of the westernmost of the Utah 13ers, deep in the High Uintas Wilderness. This image includes three 13ers, only one of which, Tokewanna Peak, has a name. It is the one most in the center that appears the tallest. It actually is the highest summit of the three, but not to the degree shown here; that's mostly an artifact of perspective.