Other names batted around for the big-screen handheld: "DSi Comfort", "DSi Premium" and "DSi Living". And Shigeru Miyamoto proposed "DSi Deka". That's according to the latest Iwata Asks roundtable, discussing the DSi LL.
There are more fun facts from this talk (translated from Japanese; the English transcript is not up yet.) Evidently Nintendo had been working on a DS Lite with 3.8-inch screens (the LL's are 4.2 inches, the Lite's are three inches, DSi is 3.2 inches). It backed off because of manufacturing cost and the success of the regular flavour DS Lite. It sounds like they also wanted to do a simultaneous release of the DSi and DSi LL but it never came together.
Andriasang has more (in English) about the discussion.