When choosing a character for transliteration, we first pick the character that sounds most similar to the English word, the meaning of the character is irrelevant,
Notice, '姆' and '母'(mother) have the same pinyin /mǔ/, picking 姆 makes more sense because it is a less commonly used character, thus sounds more foreign, not to mention 母 means mother would be worse in a man's name, at lease we have 男保姆
Similar case:
The character 菲 is often used in female names, but we use the character for transliteration of 菲比斯 (Michael Fred Phelps) and no one would question why not use 非 (not) instead.
Side note: Before President Richard Nixon (尼克松) became friendly to China, they transliterated his name as "尼黑虫" not caring about 黑虫 meaning " black worm"