No hard and fast rule, but the more respectable you were, the more you got away with. Or maybe dependant on whether the previous partner was still local!
Our small town had two (at least!) couples living without benefit of marriage, for years. One a respectable tradesman, the other in the poorest part of town. The tradesman, John Gibbs, had a failed marriage, disappeared to London for a few years and came back with his "wife" and child in tow, and went on to have a further 8 children, all registered and baptised as Gibbs. But when his "wife" died, while her death was registered as Gibbs, she was buried under her maiden name! His first wife lived in Derbyshire.
Our poorer couple, the wife was the one with the failed marriage. She started having children with Thomas Hillyer, but they were all registered under her name as Smith, with Hillyer usually as one of their Christian names. They later married, but the children were still usually called Smith, although that could vary - even when two of them joined the army! Her husband was living a few hundred yards away, until his death.