Even though we find people with two names (e.g. Doniel, Hadassah, Koheles, Poti-Fera, Kushis, Kush) these names are used in different places to represent a different aspect of the person. I don’t know of a place where two names of a person are mentioned together. It seems that in each circumstance only one name is relevant. Similarly, in shomayim, a person will have one name which may contain two words.
Since my name starts and ends with a yud, I just repeat the pasuk “Yihyu liratzon..vigoali” at the end of davening. Does anyone have an opinion on this?