10.4 is available for Mathematica users. This is not the case for Wolfram Desktop. Currently, for a Windows user, the only way to find out seems to be to download the software from the account page and when the download is finished, check the version number.
How do configure/set-up your profile or similar to get a notification when a new version is available?
I normally get a notification by mail when there's a new version out. It always lags 3 to 4 weeks.
I didn't set up any notification for this so I guess you should receive one soon. I didn't get one yet.
It is indeed odd that when you want to purchase the software there no prior indication of the version you buy (at least I can't find it either).