It depends if you want the cinematic or realistic answer. I'll go with a mix of both. The simple answer is, nobody does. The nature of interstellar travel and communications is going to put a big crimp on multi-world spanning criminal enterprises. Any kind of overlord syndicate would be extremely difficult to make happen, without it collapsing under its own weight. More specifically, the various syndicates as they exist (and continue to do so) have very real and substantial differences in history and culture. There's no way to organize all of them to come together without bloodshed inevitably being the result. At best, you'll find a a few Yakuza rengos (or Mafia/Vor/Tong equivalents) that manage affiliate kumis on a handful of worlds and engage in some sort of profit-sharing or affiliate licensing fees.
All that being said, if you want to go a lot more cinematic, there's a way to do so. But I still wouldn't recommend having one ruling syndicate sitting over all of the org-crime groups. It takes away one of the greatest strengths of these groups as a storytelling device...conflict caused by their diversity. I'd look to find that sort of multi-cultural criminal board of directors approach in the Mafia. They have a real-world history of organizing in such a fashion, extending hands to and incorporating other ethnic syndicates, as well as managing to operate under the Commissione approach. Even amongst the Mafia, the Commissione was a place ridden with internal conflict and scheming. There isn't a corollary like the Commissione to be found in the real-world history of the Yakuza, the Vor, or the Tongs. Even the larger Yakuza rengos in history may have kept the lines of communication open with other rengos, but couldn't unite under some kind of singular banner or oversight. I'd look to make one larger syndicate (the Mafia) that can present a bit of a squabbling, but united, front. It allows them have say Turkish Maffiya families in the Free Worlds League, while having La Cosa Nostra families amongst the Italian stylings in some of the Skye region.
That leads into my next point. Don't try to paint too broad. Syndicates can't be viewed as controlling territory in the Inner Sphere. They will never be able to pull the resources together to compete even on the level that mid-level interstellar corporations do, let alone governments. It's all about alliances and influence when dealing with syndicates. Influence among government or corporate officials allows a syndicate (in the real world or Battletech) to appear to have much more direct control than they really do. They'll have strongholds in traditional markets and communities (Yakuza in DC markets, for example), but you're going to find kumi-like organizations scattered around the Inner Sphere in any place where there is a significant community with Combine-like qualities. Even in those strongholds, you're talking about hundreds, if not thousands of kumis all working for their own goals. Some will unite into a few specific rengos (likely those with Black Dragon and LAW ties), and play a grander role. But they won't control the DC as a whole. They may be able to influence a lot of the DC underworld, but there's a very important distinction when dealing with org. crime between influence and control. If you're asking for strongholds to focus on? Here's the simple list.
DC - Yakuza. A few, maybe five to six at maximum, rengos with hundreds of smaller one or two world kumis/kais. Most of the rengos will fall in with the Black Dragon/traditionalists, with one or two being New Way. This leads to the New Way/Old Way conflict on a larger scale. You'll also find kumis cropping up on Solaris VII, Galatea, New Kyoto, and all of the Lyran and Davion border regions in substantial numbers. This is where they will spread their tendrils out when possible, and those border regions will be hotly contested markets between the kumis and police forces. Additionally, you'll get small regional or one-world kumis popping up scattered throughout the Sphere, having no real interaction or contact with the greater whole. They'll work fine as a storytelling device for a specific world.
CC - It's a mix here, about 60% Tongs and 40% Vor. Same rules as the Yakuza, though you'll see more conflict amongst the two CapCon criminal influences. They'll have influence on the border regions as expected, but the Tongs will be heavily combated in the Capellan March (much like the Yakuza in the Draconis March) due to the prevalent xenophobia directed at the two cultures. The Tongs that are in the Capellan (and Terran March to an extent) will be buried deep, and extremely difficult to root out.
FWL and Terran areas - I'd put this as the multi-ethnic Mafia's game, with a smattering of the Vor. Different families for different areas, to fit the regional tastes. Less focus on massive amounts of profit here, and more focus on maintaining a certain criminal culture and image.
LC - Yeah, this one is a Mafia/Vor toss up, but more likely a 60/40 split, unlike the FWL which is more 80/20. Drastically increased focus on profit, expansion, and corporate feel, with the Vor being the much flashier and more dangerous (to the public) "young turks" in LC space.
FS - Some mix of all but not a great deal. There's a number of factors regarding their intelligence agencies, nobility, and governmental structure that will make it difficult for more massive amounts of org crime to take root here. You'll see much smaller syndicates and markets here, excepting some of those hotbed border regions.
The Periphery - Wide open, with a larger emphasis on smaller, home grown groups. Think street gangs versus syndicates. This is where fun and wild local varieties come into play.