"Bloodline" makes me think of dynasties, so maybe some royal dynasty? Most of them only lasted about 4 generations though; not much of a bloodline.
The first long dynasty which popped into my head was Biblical, but it has the most ordinary name: David.
Britain's Plantagenets had a good long run, but they weren't nice people. Not only did they fight wickedly amongst themselves, but one of their kings -- possibly their first king -- was the original for the Sherrif of Nottingham in Robin Hood stories. And, possibly the same Plantagenet king is Scotland's most hated person ever! I think it was one of the Edwards... 1st... 4th... I don't know. But the Plantagenets were so long-running and re-used the same names so many times, they're the reason we put numbers after kings names. And I don't think any of the Plantagenets were quite as wicked as certain Davidic kings.
There must be lots of dynasty names you could use, and not just royal ones. Britain -- and probably all of Europe -- has these long-running family names amongst the lesser nobles. I have almost no idea which other parts of the world have bloodlines like this. Japan, perhaps? I know almost nothing about Chinese dynasties or ancient South America, and less than that about Africa or the Islamic world.
You could take a totally fictional bloodline; it doesn't matter outside the possibility of trademark issues. Do trademarks even apply to things which don't compete in the slightest? Oh... they do. Google had to pay George Lucas for "Android". Still, there are un-trademarked minor characters in obscure novels which I like and might name things after, so obscure Klingon houses also popped into my head at the thought of bloodlines.
If this all sounds a bit historically-focused, I'm going back to a possible origin of
alphabetic writing for mine.

I'm taking the letter representing making things; Kaph. A letter representing self-expression is free, but that's "Peh!"
There's an OS called Jehanne -- Joan of Arc -- because it's heretical against its Plan 9 roots. Nothing bloodline-related there; she never had kids.
zaval wrote:as long as you don't call it "bloodline", it will be ok.

or, you can tease the destiny and call it somewhat embarrassing, so it will definitely succeed for you to have a lot of blushing moments in future.

like me, for example, I wanna call my entire OS Avril, after Avril Lavigne - my crush forever.

There was a time I wanted to develop an Advanced Voice Recognizing InteLligence... for much the same reason. I wanted it to sound like her.
