Girls get flowers, gemstones, places, etc. while boys get old grandpa names.
Comrade Adam is keeping an eye on the lists and is posting highlights whenever new names are approved: https://kammeratadam.dk/keyword/godkendtefornavne
A name that really begs to be screamed out loud
What? The state gets to choose which name can you freely give your child?
People here find it very strange (insane even) that in US you can name your child Apple, North West or X Æ A-Xii.
(I don't have a strong personal opinion on this.)
But apart from that, there’s no list, you can invent names.
Denmark did use to have "These and only these names" and they were written into the law (yes, there are pages and pages of Danish legislation that are just names), but now any non-offensive name is okay, and for administrative purposes, an "approved"-list is kept for easy reference to things that have already been, well, approved.
In here, for example, the name needs approval to not be harmful to the kid, nor degrading, nor diminutive form of name can be used. Also typos are checked for.
In many western cultures [1] it was (still is, but to a much lesser degree) customary for boy's (especially for the eldest) names to be hereditary. This gives natural tendency for the set of "traditional" boy names to be self reinforcing: remain more closed and maintain relative relevance. There are simply less boys to play with naming.
On top of that, it was common for the eldest son to inherit the estate and produce more offspring, while the younger were much more likely to be enlisted and as a result suffer from early-adulthood mortality. This further reinforces the traditional names.
I wonder how these statistics would look like if it was possible to control for these effects. Maybe look at variety of names among fallen soldiers versus the general population with some time lag?
> Almost all typical boy names have a feminine version
If I were to warrant a guess, I would say this is to quite a large degree an effect of the first-born being a girl and getting a feminized version of the hereditary name.
In fact, you can almost prove it by bijective mapping to a subset. Almost all typical boy names have a feminine version (Juan->Juana, Carlos->Carla, Manuel->Manuela, Adrián->Adriana, and so on... there are some exceptions, but not many) while the opposite is not true, there are plenty of common girl names without masculine version (Carmen, Laura, Marta, Elena, and many others).
There are also papers doing the actual stats and concluding that girl names are more diverse. No idea what the reason is.