It is possible, but it’s a little bit of work. In Library > Notehead Sets, choose the Pitched category on the left-hand side, then select the Pitch Name Noteheads notehead set.
On the right-hand side, select each existing pitch notehead in turn, and click the pencil icon in the action bar at the bottom of the dialog to edit it. Delete the pitched notehead, which will reveal a filled white notehead behind it: this is important, because it ensures that the staff lines won’t show through the note name in the notehead. On the right-hand side, choose the Note name noteheads range. You will find the basic Do, Re etc. noteheads here. For noteheads that contain accidentals as well, choose the Note name noteheads supplement range at the very bottom of the list of categories. Add the appropriate solfège notehead covering the white notehead by setting its attachment point to e.g. Middle left to Middle left.
Now repeat for all of the noteheads in the notehead set.