Who is 'The Danish Girl'?

The film's title suggests the possibility of 'The Danish Girl' being either two of the lead characters, Lili and Gerda. However, whilst the story may seem to be about one of the first prominent transgender, it really becomes about the story of Lili's wife, Gerda, and her struggle with Einar's transformation into Lili. Whilst Hooper delves into Gerda's attraction to Hans, he does not really explore Lili's attraction to him. Critics have argued that the film conventionalises the story, that Hooper makes into one of charm rather than really showing the struggle of this emotional and physical change.

Does the film handle the subject of transgender successfully? Who was the real 'Danish girl' in the film?