I've added two new Web pages for some unnamed lakes published in a report by the State of Washington in 1961 and updated in 1965 and 1973, the last year adding township and range locations for unofficial names to the lakes.
There are over 400 mapped lakes in Mt. Rainier NP, but only about 50 have names, and a few of the remainder have informal or unofficial names used by a variety entities for a variety of reasons, but none of these names have been officially adopted by the Board on Geographic Names.
I haven't found reasons for the state selecting about 40 unnamed lakes for the series on the selected lakes of Washington, especially since the bulk are in the northeast quadrant, but they're in the report and now on Web pages for the description and a map of the lakes.
The majority of the lakes are inaccessible except by difficult off-trail scrambling through forest or in the upper elevations, often with extensive elevation gain or loss from existing trails. A few in the northeast quadrant are accessible off the Palisades trail via the road to Sunrise.
I would caution folks to exercise care with hiking off-trail to any of these or any lakes to respect the environment and the lake. A little damage takes time to heal.