In Dorico, you don’t exactly change a specific notehead (even though the context menu says Notehead) – you apply a notehead set, which then picks a specific notehead based on the duration of the note and the rules of the set.
If you want to give a black notehead to a whole note, one way to do this is by defining a new notehead set (starting with your current notehead set and using New from Selection) and then removing all the noteheads from that set except for the black notehead.
Then you can apply that set to the note you want to change.
Another approach is to use a 1:4q tuplet – one quarter in the space of 4. This will let you enter a quarter note that has the duration of a whole note. Then you can hide the tuplet number, and hide the note’s stem in Engrave mode.
It is not about a musical document (a practical score) but about making musical examples and educational documents in which for example you may need to highlight any note in a scale of whole notes by changing it from white to black.
This kind of free graphical editing of musical elements was perfectly achieved in Finale with its Special Tools: you could tweak anything in the score with complete freedom.
Dorico seems to me oriented to composers, but not so much to scholars or teachers who need to design freely all kinds of theorical examples and documents, very different from musical scores.
In your case – as @asherber already pointed out – you can achieve this with a custom notehead set. I’m writing often for liturgic chants where I need a brevis notehead as a recitation note instead of a black notehead.
So I created a (persistent) custom notehead set only with the brevis-notehead and assigned a shortcut (actually a Stream Deck button running a Keyboard Maestro macro), which is pretty handy.