Hello, I am not quiet sure about the end of a formal letter. I need to know if it will be correct to finish with a simple phrase: like Greetings, and my name afterwards or a more formal phrase and my name.
you use greetings to start a letter. You would end a letter with sincerely or thank you.

Here's the very basic idea of a formal letter

Dear Mr. Smith, (Note that you don't say 'Greetings')

. .. .



Yours sincerely,

(followed by your name)