I think you are using the wrong term. Rather than “Ink Name”, I think you mean INCI name. This refers to the official name of ingredients as listed in the International Nomenclature of Cosmetic Ingredients compendium.
When you are creating a List of Ingredients (LOI) which goes on the back of your cosmetic product, you are required to list the INCI name of all your materials.
The Trade Name is a name that the raw material manufacturer gives to an ingredient they sell. They do this as a way to make their own products stand out and make it easier to market. You DO NOT use this name when putting together a list of ingredients. You may use this name when you are putting together a formula. In fact, it is probably better to use a trade name when putting a formula together so you know which supplier to use for making a formula.
I do not know what “Grade Name” means but I would guess that this is a alpha-numeric designation that the raw material supplier gives to different blends of a specific raw material. It is not really used in the cosmetic industry (as far as I know).
As an example. Consider a detergent like Sodium Lauryl Sulfate.
INCI name: Sodium Lauryl Sulfate
Trade Names: Stepanol LCP (Stepan) or Jeelate SLS-30 (Jeen)
Grade names: (Stepan) Stepanol LCP, Stepanol CFAS-70, Stepanol DXAS165P