Referring to myself in my thesis I am not an English native speaker and I wrote my thesis in English. If in the title page of my thesis I would like to write

Advisor: "The name of my advisor"

M: "My name",

then what should M most commonly be?

My choice for M is "student" but am not sure of that.

Note: The common culture of my country makes me write the title page as what I show in my question. I may very well be considered "improper" or even "rude" if I do not do that, and consequently would incur unnecessary judgements.
For any specific thesis, you should check the regulations of the institution the thesis will be submitted to. There are often strict rules about the formatting of the title page.

I've not come across the advisor being listed first. The format I'm most familiar with would be something like the following:


  Why there are no Frogs on the Moon
  
  Neil Armstrong
  
  Advisor: Dr Thomas O. Paine


There's no need to write a word before the author's name. It is understood that any title page will contain the title and the author so any name that is not explained as being something else (e.g., "Advisor:", "Editor:") must be the author. You see the same with academic papers: the authors are usually not explicitly described as authors; it's just implicit that the list of names below the title is the list of authors.

Note also that the name(s) of the author(s) usually come before any other people who have contributed to the document. Authorship is regarded as by far the most important contribution.