Nickname separate from 3 names?

My partner and I were under the assumption that the nickname would also be an official name when we were choosing names. So we thought you’d list the birth names on the declaration form and then specify the nickname (just like on some official documents for work or school, etc.). So we decided our daughter would get our mothers’ names: J.... A.... We combined those names to create her nickname: Jolie.

Now we’ve found out that her nickname isn’t officially registered anywhere, and we find that a bit of a shame. We already call her Jolie all the time; to us, that really is her name. So now we’re really torn!

Do we go with three names: Jolie J.... A...., which sounds a bit less nice because the first name starts with the same letter as the second and ends with the same syllable as the third (since we combined them. Not exactly, but phonetically it’s similar!)

Or do we stick with the name J..... A..... and keep the nickname separate?

Both our parents also have nicknames that differ from their official names, and nobody knows them by anything other than their nicknames. That makes us less worried that the name Jolie will ever “disappear” for her. But we still find it a weird idea that her name won’t appear anywhere other than on the birth certificate!

I’ve also read that it can be inconvenient when booking flight tickets, etc., but we don’t see that as such a big issue, so it’s not an argument for us.

What would you do?