To all non-Dwarves and to Dwarves when non-Dwarves can hear, he introduces himself by simply his first name: Frar.

To Dwarves, he introduces himself with his full name in the Khuzdul (dwarf) language: Frar Nazuk-uk.

In a formal setting or upon introduction to someone he respects or who is higher station than him, he will introduce himself with the common translation of his surname: Frar Bloodgranite.

Though "Frar" is Khuzdul, it is not a proper noun and acceptable to use this first name with anyone. He will only use Khuzdul with other Dwarves.