Rename a file on git and keep history

git mv oldname newname

does exactly what you want.

EDIT: Point is that I don't think the github Desktop client lets you do that. To be honest, I see less and less usage for Github desktop, seeing that a) the website of github lets you do more things directly online in your fork on their servers, and b) git integration into almost any IDE is available and c) github desktop might hide a lot of the details of handling git, but it does the "wrong thing" in my humble opinion, not only taking away complexity, but adding confusion to the mix, and d) Github's own tutorial doesn't even mention it