The Aztec word for agave is Nahuátl (or Náhuatl) Metl, or Nahuátl Mexcalmatl, from which last word the name Mezcal is derived. These Aztec names mean "magnificent".
The word agave itself is derived from the name of the mythological Greek deity Agavos ("high born").
Since there is no way uploading .xls files here, please see for Agave names and synonyms AgaveData > Nomenclature, also for hybrids and cultivars.
The synonyms at the above mentioned URL only include names with Agave; for synonyms such as Manfreda or Polianthes see http://www.agavaceae.com > Database > Agave > All published names.
The information is based on the articles of Peter J.K. Kuppen in Succulenta (see page Literature) and on various other sources. Also see attached page.
The names used at the picture site still have to be corrected.
Latest news from the nomenclature front (Eggli; see Literature): celsii should be mitis again, and vivipara stays vivipara...
For Spanish and English names see the same link here above.
The Mexican name for agave is maguey, which is derived from the name of the God Mayahuel who was believed to live in them and for whom pyramids were built.