And Beth's Days of Our Lives Page has this in Kristen's bio:
Kristen Blake is the natural daughter of Rachel Blake and her husband. She has an older brother, Peter Blake. She has been married to Tony DiMera and John Black, though the latter marriage was invalid. Peter and Kristen's parents died while they were young. Consequently, they were adopted by Stefano DiMera. In the beginning, Kristen was good and saintly. She was a devout Catholic and a social worker. But her determination to hold on to John Black's love turned her into an evil, manipulative witch.
And here is what Beth's page has about Stefano:
Stefano DiMera is the father of
Renée DuMonde, Megan Hathaway, Benjy Hawk, Lexie Brooks, and Elvis Banks. He is also the adoptive father of
Peter and
Kristen Blake, and raised
Tony DiMera believing that he was his son. He had a nephew,
André DiMera. It is unknown exactly how many offspring Stefano has. Although we've seen eight of his children and two wives, it has been said that he has others. Stefano had a common-law marriage with
Daphne DiMera, who is also deceased, and was briefly married to Ellen Hawk. He is also the ex-husband of
Vivian Alamain. Stefano first entered the show as an organized crime kingpin. Throughout the years, he has become more gothic, especially through his firm belief that he will never die. According to Stefano, he is like a Phoenix, and he will always rise from the ashes to his former glory and power. He is the seventh son of the seventh son; as a 300 year-old DiMera family legend dictates, such a son will never die. He certainly has proven this time and time again. Stefano has "died" ten times, coming back stronger than ever each time. Because of this, he holds the record in Salem for the most faked deaths.
Half the online sites say he adopted them, and the other half say he was only their guardian.
Maybe Jason47 has some official info (old scripts?) that verify which one it is.
Up until Kristen was presumed dead (when Edmund accidentally killed Penelope), she was known as Kristen Blake. I don't think she used Tony's last name when they were married.