I think its going to be whatever you decide. IIRC, the last Bloodname list we have is from Wars of Reaving, which is 60 years off what you're going for. Those that are limited to 5 or fewer bloodheritages at the time of the WoR might be back to full use by the time 3145 rolls around, we just have no way of knowing.
What constitutes Greater or Lesser is going to be whatever you decide. I mean, someone might consider Fletcher a Greater Bloodname, but on the other hand, maybe Malavi's actions before the Jihad have pushed it back into the lesser status by 3145.
You could look at the various HH commanders in FM3145. That might give you an idea of how well the various Bloodnames are doing.
There are three Star Colonels with the Cooper Bloodname in the Hell's Horses forces, but surprisingly, a Galaxy Commander in the Wolf Empire, a Star Colonel in the Wolf Empire, and 3 Star Colonels in the Raven Alliance. It seems like that might make it non-exclusive now, but for all we know, those are Hell's Horses units that were taken in battle, rather than them having the rights to the genetics.
3 Star Colonels bear the Fletcher surname.
Houan is the Bloodname of Theta Galaxy's Galaxy Commander.
2 Star Colonels have the name Seidman.
So that doesn't really help alot, but indicates that they're still around and being used atleast.