If both kanji existed in China with the meaning of “head” before they got borrowed into Japanese, it’s more like they just are two kanji that mean かしら and so you could use them to write かしら.
Why 頭 exists when a perfectly good simpler kanji that means the same thing existed is another question, but it wouldn’t be the only one in that situation. 北 started as a picture of two people facing away from each other with the meaning “back”, but eventually this meaning got overwritten by “north” due to sound similarities again. Eventually they just made a new kanji for back, 背.
Usually in those situations, we’re talking about stuff from way before contact with Japan was on the horizon.
The radicals actually do have real names. or at least represent an idea. Sometimes WK uses the traditional meaning, more often then not they use a sillier name to help with memorization.
I used to get really bent out of shape about this from a purist perspective, but came to the conclusion that radicals ultimately don’t mean anything in the spoken language, so why worry about it. What ever helps people remember Kanji is all that matters.