Editing to add: the COTREX site (https://trails.colorado.gov/places/na~690410) also only labels the northeast-most of the two lakes as 'Irene Lake', with the other blank.

Hi David, is that your website? I stumbled across it a bit ago and I love the idea. Appreciate the very extensive research on the name as well. The name for 'Sprague Tarn' on OSM referenced here came from Lisa Foster's book (https://www.amazon.com/Rocky-Mountain-National-Park-Complete/dp/0615526845). It is absolutely an unofficial name, but unfortunately she offers no additional details on the origin, writing only that 'an icy lake lies at the base of the glacier, unofficially named Sprague Tarn'. Regarding the dual entries of Irene Lake in the USGS online mapping data, I had noticed that as well. However, the map in Lisa's book (which she notes is also from USGS) only labels the northeast-most of the two as Irene Lake - the other is blank. I will say that USGS maps are known to contain the occasional error, so despite being the 'official' source I do view them with some skepticism from time to time. Since OSM naming rules do not require a name to be government-official, but rather just whatever is commonly in use, I feel Sprague Tarn is still an appropriate entry on the map. It has a documented history of use and helps to avoid the confusion of the two identically named lakes right next to each other (with the name Irene already being confusing enough given the presence of Lake Irene on the other side of the park).

No issue with changing the tags as you described. Go for it.

That was inadvertent. I have updated with the brand-specific tags now.