The question is simple if an effect caused Morophon, the Boundless' enter the battlefield effect, "As Morophon, the Boundless enters the battlefield, choose a creature type.", to trigger twice would the second choice replace the first choice? Or would they both stick?
Morophon, the Boundless' second ability is a replacement effect:
614.1c Effects that read “[This permanent] enters the battlefield with . . . ,” “As [this permanent] enters the battlefield . . . ,” or “[This permanent] enters the battlefield as . . . “ are replacement effects.
Replacement effects don't 'trigger' and AFAIK there is no way with the current Magic cards to make them apply twice. Yarok, the Desecrated only duplicates triggered abilities, not replacement effects. One of the rulings below the card in Gatherer mentions this as well:
Abilities that apply “as [this creature] enters the battlefield,” such as choosing a color with Diamond Knight, are also unaffected.