Parents' names only became compulsory with civil registration in 1837.
In 1836, most churches would be using pre-printed registration books, especially in a busy place like Liverpool. Because there was no requirement for it, space for naming parents was not provided.
What you commonly find, though, is that one or more of the witnesses was a sibling - still common today. Using a sibling can give you a good idea which are the likely parents from the pool of baptisms.
It was the bride and groom who were deemed important, so sometimes you get occupations noted. This would help cross-check with later census info - and don't forget that sons often followed their father's trade.
