Do Japanese names use onyomi or kunyomi?

I have trouble reading Japanese names with characters that I have known and been able to recognize for a long time.
Do they use onyomi or kunyomi in the names? This is what I tend to confuse... Thanks!

Mostly Kunyomi but sometimes Onyomi and others called "Ate-ji"(which unable to pronounce neither Kunyomi nor Onyomi).

Thanks!

By the way,
pronunciation of Japanese names are unsettled, so even Japanese can't read all names correctly.
For example, 高田 is commonly pronounced "Takada" but some named "Takata".

In Ate-ji, though it's an extreme example, 小鳥遊 is very famous, it's pronounced Takanashi (means "No hawk") beacuse of little birds playing.
小(little) chii, ko, shou
鳥(bird) tori, chou
遊(play) aso, yuu
And 鴨脚 is Ichou (means "gingko") because duck's leg looks like ginkgo biloba leaves.
鴨(duck) kamo, ou
脚(leg) ashi, kyaku
The personal name, 一 is often pronounced Hajime (means "the first").
一(one) hito, ichi
Who can pronounce this without explanation?

This reminds me of first names in English mispronounced by people that don't speak English and non-English names butchered by English-speaking people..

Yves is a boy name in French, pronounced Eve...
Jean, another French boy name--and only used for boys, is pronounced differently by the French and the English..

Thanks guys!