Dan Fingerman '69 (firstname.lastname@example.org):
Random Hall was officially dedicated as an MIT dorm on Leap Year's Day of 1968. Present at the ceremony, if memory serves me, were then MIT President Howard Johnson and Dean of Students Ken Wadleigh, together with a variety of other dignitaries. We chose Leap Year's Day as the official opening of the dorm so its birthday would fall only once every 4 years, eventually making it the youngest of all of the dorms.
I forget how many students (all male) lived there at first, but I know it was full. It had been taken over by MIT to house an overflow of students needing campus housing. I don't know how long it actually served as a dorm that first time around, as I graduated in 1969. I suspect Mr. Yamane is accurate about the housing for visiting faculty and more recent history of Random Hall, but I do know about the earlier history -- I lived there in '68 - '69 and I was the founding President of Random Hall.
For what it's worth, Random Hall was originally going to be named "Random House." Dean Wadleigh & I sent a joint letter to Bennett Cerf, then head of Random House Publishers, inviting him to the dedication ceremony. We received a "cease & desist" type letter from Random House legal folks. It became Random Hall, named, of course, in honor and memory of J. Arthur Random.