His known names, usually given to him by various peoples:
-Gandalf ("Elf of the Wand", though he is not an elf) by various peoples. Titled as "Gandalf the Grey" and "Greyhame" or later "Gandalf the White".
-Mithrandir (Sindarin "Grey Pilgrim", "Grey Wanderer") from the Elves, also used by the Men of Gondor.
-Tharkûn, from the Dwarves.
-Incánus, from somewhere in the South.
-Olórin, which he was called in the West in Aman.
He has also been called various other things, some of therm derogatory, although they are not used as proper names.
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Gandalf was known by different names to different peoples: Gandalf to Northern men, Mithrandir to the elves and Dunedain (as in Gondor), and Tharkun to the Dwarves. Olorin was his true name as a Maia.
They all look different They have different colored hoods.
Frodo knows Gandalf because Gandalf was like Bilbo (Frodo's grand-uncle) guardian on Bilbo's adventures. Now, Frodo knows Gandalf through Bilbo.
Wood mostly, I think. But of course, it is a magic staff, after all, so we can't be completely sure.
Gandalf has several names, depending on the language of those he is dealing with:Gandalf - Common Speech; used by men, hobbits, etc.Mithrandir - Sindarin; used by most elvesOlorin - Valarin; used by the Valar & Maiar in the Undying Lands (his original name, as he is of the Maiar)etc.