If a star is found to be multiple how are it's various components designated?

Answer 1

In visual doubles the primary is designated A and the secondary B. This is by definition the most massive, but until the mass is determined it is the component which is brightest in the wavelength (color) in which it was first seen to be double.

When a third component is found it is often given the designation C.

Sometimes the third component is often a closer component to A or B. While these are sometimes given the C designation, sometimes they are so close that the form a stable hierarchical system. If the third component were found beside A, for example, this system would be called Aa,Ab where Aa is the primary of that subsystem and Ab is the secondary. In this circumstance, all the previous measures of AB are understood as being made from the photocenter of the Aa,Ab subsystem to B.

If a fourth component is found close to Ab, for example, the designation of this pair would be Ab1,Ab2. At higher levels the system of lower case letters and numbers would alternate.