I admit I didn't know about the Ibsen connection; the reason I think A Doll's House fits just a bit better is that the myriad "bits of music," and much more individual songs, lend themselves to this sense of things occurring in different rooms, separated from each other. (I love the album, of course, in case I'm coming off wrong. A title's not very important, really.)
From a lot of stuff I've read, the album's cover was so striking at the time because of the drastic, and quite smart-ass, contrast between the plain white square and the trend-setting Sgt. Pepper image from the year before. I think the Beatles' acute sense of humor is often left out these days!
Artist George Hamilton came up with the idea, and his original thoughts included the ring from a coffee cup. Paul thought that was a bit TOO flippant, so the embossed name of the band was settled on instead. "Has there ever been an album just called The Beatles?" Hamilton asked. "I don't think so, but I'll have to check," said Paul. (That's a funny thing, but of course the Beatles couldn't keep track of all the bastardized USA album names that Capitol had concocted.)
Then they thought about having the green smear of an apple on the cover, as if someone had thrown...well, the Beatles' new logo, I guess, at the whiteness. This was abandoned as well, since the quality of the printed image from country to country couldn't be assured, and a green apple smudge would just look like a bit of dirt without the resolution.
I guess my favorite quote about the White Album is Paul's, from Anthology.
"I'm not big on that, y'know. 'What if we'd done this or that....' It's great. It sold. It's the bloody Beatles White Album! Shut uuuup."