The general rule to abbreviate each month is simply to take the first three letters in each one, which makes it easy to remember and to put into practice.
A month is defined as a period of roughly four weeks, which makes up one of the twelve periods that form a year.
Technically speaking the word, the word month doesn’t have a synonym, and neither do the individual months of the year. This is large because they are proper nouns.
Abbreviations, as a rule, are only meant to be used when it’s important to save space or avoid constant repetition.