I usually list the name that the company was when I worked there, and if room "(now New Name)." If it's a place that I find particularly releveant to the job I'm applying for, it's something to mention in the cover letter. It also depends on whether they were known better as the newer or older name. I worked at the Tennessee Repertory Theatre when it was under Equity's LORT agreement, it's now the Nashville Rep and SPT with one LOA to LORT per year (lower tier contract now). I like to point out the higher one, in my case.