I gather I would just tell the desk, when checking in, that I need the bed pulled apart and made up separately into the two twins -- no big deal for them, I am sure.
Right.
If as
Lurker says...the room has the kind of King that separates. I do this all the time in Europe: Request that the "King" be split into 2 Singles. Though I do it mainly because this allows for better availability of Suite upgrades when traveling with a non-same-bed companion, in that there seem to be more Suites listed as "King" than as "2 Singles." This way we get the Suite upgrade plus separate bedding. It usually only takes a few minutes to get a maid up to the room to split the bed into 2 Singles.
In fact here's a photo of a split-King from the Sheraton Park Lane in London (where I was sharing a room with another FlyerTalker, as it so happened). You can kind of tell in the upper left photo that it used to be a King because the beds now extend slightly past the King headboard:
http://members.aol.com/premexfiles/sherLONpark428.jpg
I've done the reverse as well. My ladyfriend and I find availability someplace we want to stay, but they only have "2 Singles" rooms available to book. We book that and then when we request a King at check-in, if they don't have a true King available, they always offer to have a maid come up and convert the 2 singles into a King (or Queen or whatever that makes it).