Is there a way to change the default notehead to write harmonics for strings or has it to be yet implemented?
We don’t (yet) have automatic support for showing a different notehead for a harmonic, but you can right-click a note and choose the desired diamond notehead from the Notehead context menu (or in the main Edit menu, again in the Notehead submenu).
Would you use the White Diamond notehead?
Since noboday has asked me specifically, I would definitely use the WIDE DIAMOND NOTEHEAD notehead… 
I’m working on a piece that has similar harmonic notation this section of Saariaho’s Sept Papillons (see screenshot). I’m just starting to engrave it into Dorico and also (finally) exploring the new harmonic features from Dorico 3 (it’s been that kind of few months where I haven’t had the time to explore all the amazing new features we got in 3.0).
For now, I should just change the noteheads manually? I assume there is not a way (yet) to change these natural harmonics using a built in function?
thanks!
The vast majority of those harmonics should be achievable directly in Dorico 3 by inputting the notes at the desired staff positions, then activating the ‘Harmonic’ property, choosing ‘Natural’, and then setting ‘Style’ to ‘White diamond notehead’.