What are some ways to get the nn Dani...

[teacherma]

Danaë
Danuta (Polish name, typically nicknamed Danka)
Danya / Dania
Edana (The Irish feminization of Aidan "fire")

Maybe a name combo where the first ends in a -da and the middle name begins with a ni-. Something like Ada Nicole could stretch into Dani.

[ashthedreamer]

The only one I haven't seen yet is Danette/Dannette. I'm not a huge fan personally, and I'm not sure it really fits your style, but it is interesting. I like @teacherma's idea of something like Ada Nicole, nn Dani.

[aureliagwendolen]

I love the name Edana a lot, but I'm worried it's too close to Edna, which is (sadly) more well known and a lot uglier.

Gwendolen nicknamed Dani is an interesting thought. I also like the suggestion of Ada Nicole (not really something I'd choose, but a great idea). I could definitely do something like Miranda Niamh.