Not only Japanese names need a phonetic equivalent - what about Chinese, Hebrew or Arabic names? Wouldn't it be more clear if Microsoft calls it "Phonetic name" or something similar? I guess that would be understood by more people without needs for training
themselves Japanese.
Besides - "Yomi" has another meaning which is basically Death or Road to Death, in some east Asian cultures including Japanese. That may have put off quite some people from using this contact product for something else like google contact.
I don't know why "yomi" was chosen, but here's a Japanese explanation.
First off, it's important to note that Kanji is not Japanese; it's Chinese.
The kanji 訓 (one kun reading is "yo.mu") means "instruction, Japanese character reading, explanation, read."
訓む ("yomu") means to "pronounce kanji using the native Japanese reading."
読 (kun readings "yo.mu" and "-yo.mi") means "read."
読む ("yomu") means "to read" and 読み ("yomi") means "reading."