You know some plate armor are not full plated armor, so I was wondering if there was a name for the soft parts. In the above picture, we see the soft part, but the guy is wearing an undergarment. Some armors have their own undergarment that seems to be part of the armor. I don't know if that's the correct wording, but the color of the undergarment and the armor matches unlike in the above picture, so I was wondering if there was a name for the soft part of the armors in the case there's a special undergarment or light armor that came with the plate armor or was part of it.
The light-colored garment worn unde the plate in the picture is a Gambeson or arming doublet.
More or less thick and sometimes hardened leather was worn under metal, or in thhose places where a given form of armor was not metal (metal armor was quite expensive, and also quite heavy to wear).
Cuir bouilli or boiled leather was worn either instead of or in addition to metal armor. It is leather that has been hardened by boiling it, and sometimes in other ways as well. The term refers to the materiel, not to any particular shape or location.
The undergarment typically worn underneath plate armor is called a gambeson (note that many of the terms related to armor are adopted from the French). It can also be called an armoring doublet, or aketon, with specific points to attach the armor pieces.
Mail was typically worn underneath earlier plate armor, to protect the weak areas that were not covered by metal. Later, full suits of armor covered the entire body, rendering this unnecessary.