Don't read the front side of your paint tubes! Many manufacturers use brand-specific color names (Winsor and Newton has many, for example, such as Winsor Violet, Winsor Blue, etc). This is a way of generating brand loyalty; customers believe that a color is exclusive to that one brand. When in reality, these colors are made with the same pigments that every other manufacturer uses.
The best way of finding out what's inside your paint is to look at the back. By looking at the pigments listed, we can find out exactly what is inside. Referencing W&N again, we can determine that the pigment used in Winsor Violet is really just Dioxazine Violet, which is widely available elsewhere.
The Old Holland tube above is made with Zinc Oxide (PW4) and Titanium dioxide (PW6).
All artist's grade oil colors will have the pigments listed on the back side of the label. Many brands will also list the binding oil(s) used. This is your ingredients list. Some brands list out the name of the pigment, some will just list the shorthand code. This shorthand code is universal and consistent between brands. The Color Of Art has an excellent database which lists all the different pigments and their properties.
By paying attention to what pigments are in your paint, you can make more informed decisions about your supplies.