Is there a word for refusing to call things by their name out of fear?

Some examples:

• "He-Who-Must-Not-Be-Named" or "You-Know-Who" for Voldemort of Harry Potter fame
• Him in the Powerpuff Girls
• Any of the various monikers for Yahweh
• possibly "She Who Must Be Obeyed" for Hilda Rumpole

Solution 1:

How about nomatophobia or onomatophobia, from Random House:

a fear of names or other words because of their meaning

Solution 2:

Taboo words are those avoided because of some stigma.

The stigma is usually cultural, arising out of can be fear (via cultural associations with bad magic or evil in the local religion, like devil or hell), disrespect (holy words that could be used blasphemously, peoples first names that you don't know or who are older than you), sorrow (names of the recently dead (some cultures prohibit the reuse of names of the dead, but some, in the opposite of taboo, make sure to reuse the name of the recently deceased with a recent newborn).

This is just an explanation of taboo -names- and could be expanded considerably for taboo words.

Solution 3:

Aside from Mitch's excellent suggestion, these terms are applicable:

• euphemism — a mild or indirect word or expression substituted for one considered to be too harsh or blunt when referring to something unpleasant or embarrassing
• object abstraction (or simply abstraction) is a linguistic term for using a more generic term instead of a specific term. This includes using "it" in phrases like "Don't talk about it — you know, it."
• sacred or sanctity can apply when the revered object moves into a scope that is much, much larger than the speakers. Namely, the fear is of something unhuman or immortal.

Euphemism in particular really matches up well with the behavior. Its application may be a bit too broad but the emotions are all there.