Just my opinion. There's one contingent of Mandrills that I think represent a greatest single source of Inner Sphere bloodhouses in any meaningful quantity.
On Arcadia, right at the start of the Wars of Reaving, the forces of Kindraa Payne-Beyl-Grant landed on Arcadia and challenged the Ghost Bears. The Bears crushed them. That Kindraa ceased to exist (as far as we know, albeit their warship fleet might have carried the banner longer). Shortly after that the Bears left the Homeworlds.
If the survivors were scooped up and made bondsmen, that could represent a decent number of bondsmen who might have had qualms/regrets about the Wars of Reaving events in due time.
Also, historically speaking, many Mandrill bondsmen were uncooperative specifically because they wanted to be reclaimed by their Kindraa. For these Payne-Beyl-Grant warriors who watched their entire Kindraa's touman get destroyed, they might have recognized the futility of that line of thinking and so lose a critical source of motivation to BE uncooperative with their new Clan.
Who in turn might have found common purpose with the Bears over the rumors of Clan Wolverine survival that Stone stirred up among the Bears. Enough for some of those Mandrills to set aside any bitterness they may feel and devote themselves to regaining their warrior status and go Wolverine hunting with the Bears. Regardless of how that ended, it might have been enough of a push of solidarity in the face of a perceived common cause.
Though ironically, any such former Mandrill warriors motivated in such a way, are just as likely to have ended up among the Clan forces that join the Coalition and from there they could have ended up as part of the Republic. Therefore, not forming a new Bloodname House but becoming part of that movement toward the dream Stone laid out.
I know that sounds perhaps too cooperative for the uncooperative Mandrills. But that era and everything they experienced changed a lot of people. We know a lot of Clansmen who otherwise would not have been moved to leave their Clan did exactly that. Transformative eras like that have a way of challenging and crushing existing preconceptions and assumptions. Anyone who lived through all those years, all those very dramatic events, was undoubtably changed by the experience of it. I think it's more than enough for any decent writer to work with to bring some Mandrill-origin characters or Bloodname Houses to life.
I still regard the odds as slim, because of how destructive that era was, and how many people simply did not live to see the other side of the Wars of Reaving/Jihad era. But not zero.
Also, I'm in camp of "I could take it or leave it." I don't think longevity into the more current eras is necessarily that big a deal. You aren't following the Mandrills anymore, you are just following people who happen to have some Mandrills on the family tree generations ago and share a surname, it's not the same. It reduces the Mandrill presence to little more than an easter egg in Battletech references. There to the delight of a few fans who enjoy spotting the easter egg. Little more.
But in theory, if someone was looking to do it, what I described above is one possible path.
