Hello TIYA.  I can tell you are acting in good faith in your edit in name placing but I am skeptical that the best course is to rename the lake. 

The first reason is that if the lake is more of a unnamed tern then it should have no name instead of eagle lake as it was previously labeled.    

The second reason is that if it is a colloquially known name that isn't named in another map, it would follow that it might be called Eagle Lake since it is the most headwater body of Eagle River.  If you rename this lake as a new placemaking effort, which is not encouraged, it would follow that you might introduce confusion by naming it anything other than Eagle Lake. If there is another lake in the neighboring valley named Eagle Lake that is still there added even more confusion. 

Third, while I honor your effort to restore the Dena'ina people there is an ironic toponymic colonialism in it as well... Mendenhall recorded natives calling this area Yunkla Creek in 1900 but this was it related to the settler's name for it as Eagle Creek/River.  The recorded native name for this river is Nuk'elehitnu. If you were going to rename this lake, The above is referenced in Shem Pete's Alaska.  I would recommend this name instead if renaming the lake was necessary.  