Strictly speaking, you can choose any reading for any kanji. (The only rule is that the reading has to be in hiragana. Well, and the rule that there are certain names or kanji that are off limits, like あくま.)
Typically, there is a loose connection between the kanji and the reading, usually (part of) an on'yomi or a kun'yomi.
I think this is more true for female than for male names, though. Male given names with more than one kanji are often read with the full on'yomi, e.g. 勇太郎【ゆうたろう】, 昭吉【しょうきち】, 快【かい】. There are also names with kun'yomi, e.g. 理【さとし】, 正明【まさあき】.
But, there are certainly names containing kanji with both on'yomi and kun'yomi, e.g. 秀輝【ひでき】, 亮介【りょうすけ】. (すけ is a common suffix for names, derived from kun'yomi たすける with quite a broad range of common possible kanji: 介・助・輔・佑・亮.)