Gabriel takes on the surname "Belmont" because of his love of the mountains.
"Some years ago, a child was found on the door of one of the Brotherhood of Lights convents. It is not known who his original parents were though some suspected he was an unwanted bastard from a local wealthy landowner, most likely the Cronqvist family though this has never been proven.
The order gave the nameless boy the Christian name of one of the blessed archangels, Gabriel and raised him as one of its own members. The precocious child quickly proved to be extremely talented, developing a mastery of the fighting arts unprecedented in the Brotherhood.
Gabriel took the surname of Belmont, after his love of mountains and the high places of the World. "
However, as you can see from the same description, he may in face be a descendant of the Cronqvist clan.
So, with these two being story facts, we can arrive at some conclusions:
1. Gabriel's "Belmont" surname has NOTHING to do with the actual "Belmont" family line of vampire hunters... unless he is the start of such a family. Without Marie, however, that seems unlikely. Note: If he has a child with someone else after the events of LoS, an unlikely but not impossible scenario, then we can lay some merit on the theory. However, with nothing mentioned, there is little to no room for an assumption at this time.
There 'could' be a Belmont Family already existing in the LoS Timeline. However, that family would be completely unrelated to Gabriel. Thus, he cannot be 'the father of the Belmonts', as mentioned here.
It is also possible that Gabriel had a bastard child with someone else while being away from Marie... but that, too, seems unlikely, as her character entry tells of her being childhood friends with Gabriel, and them being married out of love. It would defeat the purpose for him to have cheated on her, what with him going on the entire LoS quest to save her out of love.
"I love you so much I risked my entire existence to free you from torture... but a couple of years ago I cheated on you with this hooker." <---UNLIKELY