You're thinking of the name Maxine, which was most popular in 1950. A maxim, on the other hand, is a concisely expressed principle or rule of conduct, or a statement of a general truth. One synonym for maxim is saying.
What is maxim? I think it's a female name but I'm not sure.
In François Voltaire's Candide, the eponymous hero attends a dinner where there is a fairly long discussion of what constitutes a good tragedy. One especially impressive and apparently well-informed scholar opines:
There are very few good tragedies; some are . . . demoniac dreams in barbarous style, interrupted in sequence, with long apostrophes to the gods, because they do not know how to speak to men, with false maxims, with bombastic commonplaces!