Azizi, Gaeilge, Gaelic and Irish are names for the Irish language, yes.

Lee isn't an Irish name; sometimes you hear it used nowadays, but it's an importation from the US.

If you look on Google for "English-Irish online dictionary" you'll find a couple of dictionaries online that will give you words in Irish for any word in English.

Eoin or Eoghan is the usual Irish version of the name John; Seán is also sometimes used as a translation. It's a man's name.

Some people in Ireland are now using traditionally male names for girls - for instance, calling girls Dara or Naoise - but usually if they want to use "Shawn", a re-importation from America, they add an "a" at the end. I've also seen some trendy types spelling their son's name Shaun or Shawn.