What is Gimli's father's name?

Gimli's father is Glóin, the Dwarf also known as one of the members of Thorin Oakenshield's company in The Hobbit. In English-language text, his name is often written without the accent as Gloin.

Glóin belongs to Durin's Folk, the Dwarves descended from Durin the Deathless. After Smaug drove the Dwarves from Erebor, Glóin joined Thorin's quest to reclaim the Lonely Mountain. Decades later, he travelled to Rivendell with Gimli to seek counsel about a troubling message from Mordor.

That meeting connects The Hobbit directly with The Lord of the Rings: Glóin is a surviving member of Bilbo Baggins's adventure, while Gimli becomes one of the nine members of the Fellowship. Gimli is therefore not merely another Dwarf from Moria; he is the son of a named character from Tolkien's earlier story.

A common mix-up is confusing Glóin with Balin or Dwalin. Those Dwarves were also connected to Thorin's company, and Balin later became Lord of Moria, but neither was Gimli's father.