After the first two episodes, we still don’t know. Darlene said she is without a partner—avoiding name(s), gender(s), and the parentage of her children. Roseanne (or was it Jackie?) said Becky’s unnamed husband died.
Harris’s age has been retconned to high school frosh, and Mark is probably named after his dad, uncle, and/or biological father.
The actor who played Mark is dead, so TPTB could either recast the role, make Mark Becky’s dead husband, or have Johnny Galecki play Mark as the father of one or both of Darlene’s kids. Yes, that sounds farfetched—but so is Roseanne saying grace and voting Republican, or Andy being MIA.
It would allow Galecki to play a character that’s nothing like Leonard Hofstadter. And Darlene could make a wisecrack about Harris’s height. (Sidebar: I love Emma Kenney on Shameless, and think she’s well-cast here.)