Gandalf
Mithrandir
Incánus
Tharkûn
Olórin.
Hasupada.
( Writings about Gandalf are only concerned about the Wizard Gandalf, not about who he was known as to the Eldar, Valar, and Maiar in Valinor as the Maia Olòrin. )
In Middle-Earth Gandalf sought no renown. His triumph was in the uprising of the fallen, and his joy was in the renewal of hope. The name of Gandalf in the Blessed Land was Olórin. In Third age, during the adventures of Bilbo in the story "There and back again.", Gandalf found the sword Glamdring in the cave of Bert, William, and Tom, and he wore it throughout the rest of the Third age and in the War of the Ring. Gandalf seemed the least of the Wizards: he was less tall and more aged, grey-haired and grey-clad, and leaned upon a staff.
Mithrandir was the name he was given among the Elves; translated to our tongue this would mean Grey-Wanderer.
Incánus was the name he was ( maybe ) given, very early after his arrival to Middle-Earth, in Gondor. Well, Gandalf did not say it was given to him in Gondor, but that was what he was called in the South. In the early years of the T.A., ancient Gondor stretched much further South than in the period where the tale of the great ring-war unfolded. Men from Númenor had explored the coasts of Middle-Earth far southward, and settlements beyond Umbar had been established. But they were the first to be absorbed in the years to come. Note that Harad (far or near) just means South. The name Incánus is / was a devised Quenya name: it is not a directly original Quenya, or Sindarin, word but a constructed one, made of the Quenya elements in(id) = Mind and Kan/Cànu = ruler / governor / Chieftain. But, for whatever its source, it later became obsolete and was only remembered by the learned in Gondor. As a curiosity it can be mentioned that in Thain's Book, there was a note saying that it is a form (adapted to Quenya) of a word in the tongue of the Haradrim, simply meaning North-spy.
Tharkûn was the name he was given among the Dwarves and it is said to mean Staff-Man.
Hasupada was a name for him in Rohan. It derives from the old English word Hasu-, inflicted Hasw-, meaning grey or ashen.
Gandalf wore a blue high-pointed hat, a long grey cloak, a silver scarf, and big black boots. He had a long white beard and huge bushy eyebrows.
3 Age.
T.A.1000. Gandalf came to the shores of Middle-Earth as the fifth and last of the Istari around T.A.1000 and he appeared in the West early in the 1100 century of that age. At his arrival, he was welcomed by Cirdan, who, from their first meeting at the Grey Havens, divined in him the greatest spirit and the wisest. Cirdan gave to him the Red Ring Narya, that he had kept safe at Grey-Havens, and that he himself had received from Gil-Galad.
T.A.1100-?. According to the Earliest Tales Gandalf brought with him, as a gift from Yavanna to Galadriel, the Ellesar.
T.A.2850. Thráin II. is kept as prisoner in the dungeons of Dol Guldur and he perishes there in torment in 2850. But before he dies, Gandalf enters the dungeons and finds him. Thrain II is too close to death to even remember his own name, but he hands Gandalf a map and a key before he dies.
T.A.2941. Gandalf saved Bilbo and the Dwarves from Tom, Bert and William in Trollshaws. He finds Glamdring in their cave and uses it later to kill the Lord of the Mountain-Trolls in Hithaeglir. After he brought the company to Beorn he left Thorin II, Bilbo, and the other twelve Dwarves at the Forest Gate into Mirkwood. He went to the Council of the Wizards, at which time Sauron was expelled from Dol Guldur and Mirkwood. Then Gandalf journeyed to the Lonely Mountain where he found dark clouds gathering and a battle being prepared.
Related links.: Battles.: Battle of Five Armies. Misc.: The Istari. Encyc.: Gandalf.