When did Khazad-dûm become Moria?

[Cúthalion]

I've always assumed that the name Moria("Black Pit") came about after the Balrog appeared in 1980 of the Third Age... and the Dwarves abandoned their home.

However... two things have come to my attention pointing to Moria being used already in the Second Age.

1. The West Gate, made by Narvi and Celebrimbor sometime before 1600 in the Second Age, read:

The Doors of Durin, Lord of Moria. Speak, friend, and enter.

2. In the chapter "Disaster of the Gladden Fields" in Unfinished Tales, which takes place in the second year of the Third Age, it also referred to as Moria by Isildur and others. When they are ambushed, Isildur says:

"There is cunning and design here! We have no hope of help: Moria and Lórien are now far behind..."

When and why did Khazad-dûm earn the name Moria?

 

[Greenwood]

This question has been raised before. You might find the comments in the thread The Black Chasm (here) of interest.

 

[Wraithguard]

Or instead I can tell you.

Moria was the usual Elvish name and was used more often after the Balrog was freed.

 

[Eledhwen]

Galadriel used the Dwarvish name when talking to Gimli. It won his heart.

 

[Alatar]

The black chasm is a good thread, i rember that no concluion was reached.
Cúthalion I never though about your seccond quote before, puts a new veiw on it.