Why do the Taiwanese have such strange characters for names?
TL;DR
Because some "fortune tellers" would suggest these characters.

Lots of parents go ask fortune tellers for names before giving birth to their children.  Now young people in these generation seldom do that, but some of their parents(the children's parents) still ask them to do that.

And sometimes, for example, fortune tellers would suggest that there should be some "火(fire)" in the baby's name because that child will be too tender. 

Not every Taiwanese believes in this, but some really do.