You seem to be well versed in heresies. Which one is "Jesus isn't special for agreeing to sacrifice himself for human sins, nobody else just got an offer"?
Christian theologies that deny the doctrine of the Virgin Birth and hold that Jesus was an ordinary man who was adopted as God's son during his life – often at his baptism, though some strands place the event elsewhere – are broadly grouped under the heading of "adoptionism". We'd need to get a lot more specific about the particular theological claims being made to narrow it down any more than that.
As is always the case with Christian heresies, it's tough to pin down exactly how commonly adoptionism has actually been practised, as most surviving descriptions of it come to us via its critics, and early Church authorities were notorious for making up guys to get mad at. However, in the case of adoptionism in particular, we have pretty solid evidence of widespread practice prior to the First Council of Nicaea, and the argument can be made that it was the majority view in at least some Christian communities as late as the 5th Century.
(Interestingly, some contemporary Mormons also hold adoptionist views, though their version is distinct from what you're describing, as it involves Jesus being adopted as God's son at birth, not later in life.)
