According to his Street Fighter Zero 3 Double Upper prologue:
Eagle, a bouncer from Great Britain who’s a bojutsu expert. His desire for the title of Dalyell Baronet has set his eyes on the world.
With this in mind I started reading up on what is the meaning of Dalyell Baronet. Turns out it’s a real thing.
Long story short, it was a title set up in 1685 for Thomas Dalyell, a Scottish general. The baronetcy was set up to always pass to his eldest male heir if present, but failing that, interestingly, could go to tailzie. Which means I
The title could pass to someone arbitrary, not a blood relative.
Now, according to Tiamat’s Plot Guide:
His bio in both the Street Fighter Fanbook and All About Capcom say he’s an inanimate, coldblooded and cruel bodyguard for a newly-rich noble family’s bodyguard.
These two sources taken together sound to me like the Dalyells are most likely the royal family he works for, and he may be made the next baron if he does a good enough job for them.
It could also mean, since they imply he is homosexual so much, that his partner is a Dalyell, and he hopes to inherit the title that way (wouldn’t be any heirs born).
Of course it could also mean he has Dalyell blood and is a legitimate heir (with the talzie stuff being irrelevant) but that seems unlikely to me because:
1: Seems like they would have mentioned he had royal blood.
2: The talzie is somewhat unique for a baronetcy, why pick that particular unique title if it was irrelevant.