I am trying to find the name or designation of this type of graphic. Is there a certain name for this style or type? I want to create something similar but am having a hard time finding more examples.
This effect in the image posted is about water color effect.
This effect can be brought about by a mixture of Pantone Colors.
The colors used will be CMYK and RGB depending upon the quality of printing and material of printing.
As Scott indicated in the comments, the term 'Oil Color Swirl' seem to describe your image pretty well.