sorry that I could not come-up with a better title...
The readings of the kanjis in a person's name, is theoretically arbitrary. But in reality, a kanji tends to have a set of maybe 3 or 4 probable readings when used in a name. For example: 伊, under the "Japanese names" header, has the following probable readings: "いと、これ、ただ、だ、よし". So, what is the official name for that set of readings?
a kanji has:
(-) ??? 読み <--- set of the most frequently used readings in people's names.
what is the set name?