One of my daughters has kept her maiden name after marrying her long-term partnet, but they have no children (and she is too old to start now). I know of one illegitimacy in my direct line, a 3x Gt grandfather, but he was Scottish and things were different there in the 1750s. He freely admitted it (so presumably his natural father had "acknowledged" him, which was enough) but it didn't stop some of his Scots/English descendents being totally shocked. According to some correspondence on the matter "The Aunts (probably his daughters) refused to discuss the matter" when asked. A pity, as they probably knew who the father had been.
Another of my direct ancestors was born 4 months after a marriage.
One was transported to Australia for assaulting a Gamekeeper while poaching, leaving several children (including my Gt Gt Grandmother to be) and his wife behind. When he decided not to return after his 7 years abroad, she produced 4 more children.
One ancestor (in Norfolk) acknowledged that a child was his and a note was put in the baptism register. He later married the mother, after his wife died, and they had another child.
There were plenty more illegitimacies in that particular branch, but none in my direct line. One lady was a "serial offender". Perhaps her beau was still married to someone? Divorce was often not possible.
Both my husband's parents were illegitimate. Through DNA my daughters now know who one of their missing Gt Grandfathers was, but the other is still uncertain. We do suspect he was Welsh and have a good idea of the possible surname, but no positive identification. My f-I-L used his mother's surname and his step-father's Christian name, when he married, to complete the "name of father" box.
Happily, regarding my Scottish progenitor, the "sins of the father" did not go beyond the 3rd generation. A Great Granddaughter from one of his marriages married a Baron!