What symbol is used for the moon when doing calculations? When doing calculations the mass and radius of the Earth can be represented by $M_{\oplus}$ and $R_{\oplus}$ respectively.

The planets all have their own symbols which can easily be found online.

But what about the Moon ?

Usually something like $M_☽$ is given but is that standard ? Are there other versions of expressing the moon ?
There is no authorative standard - you can use what you want, as long as it is clear what you mean. Besides that: yes, ☽ is reasonably standard. Often also written indices like $M_{moon}$ or $M_m$ are used.

Also see Wikipedia with its many references.