The password that opens the Doors of Durin is “Mellon.”
“Mellon” is Sindarin for “friend.” Gandalf discovers the answer at the West-gate of Moria after interpreting the inscription and realizing that the instruction means to say the word “friend,” rather than to provide a secret military code. When the word is spoken, the doors open.
The Doors of Durin were made by the Dwarves of Khazad-dûm with help from the Elf Celebrimbor. Their design combines Dwarvish construction with Elvish lettering and imagery, reflecting the cooperation that once existed between the two peoples.
Khazad-dûm is the Dwarvish name for the realm and city later commonly called Moria, not the password. “Friendship” gives the English meaning but is not the canonical word spoken in the story.