It was called Orodruin which is Sindarin and translates to 'mountain of red flame'. Mount Doom is a translation of Amon Amarth which is what the people of Gondor called it after it errupted at the end of the Second Age (when he showed himself as reformed once again after the fall of Numenore).
Originally Posted by Aideani
No one knew what Sauron was doing when he was forging the Ring. No one even knew it was Sauron. He had taken a fair form and used the name Annatar. Also keep in mind that Mordor was not exactly Disney-land. There was no one there to see what he was up to except perhaps his own servants.
What would a Balrog do with the Ring? Very difficult to say but if it came down to a contest of wills between the Balrog and Sauron, I'd suggest it's a very even match. I'd likely give the edge to the Balrog as it's more capable of violence. Sauron always preferred to use cunning and have others do his fighting for him.
[FONT=Trebuchet MS]"You can't fight the Enemy with his own Ring without turning into an Enemy" - J.R.R. Tolkien, Letter # 81