What is the colored part of a mana cost called?
The rules don't directly define a term for this part of the cost, but they do use a relevant term in one of the rules describing cost reductions, 117.7a:


  Effects that reduce a cost by an amount of generic mana affect only the generic mana component of that cost. They can’t affect the colored or colorless mana components of that cost.


So, "colored mana component of the cost" is a reasonable term to use for the colored part of the mana cost.

You could also get a functionally equivalent effect by borrowing the wording of the Emerge ability:


  {T}, Reveal a creature card from your hand and pay its mana cost reduced by its converted mana cost: ...