In other words, what's the word for not wanting to repeat a word? I find attempts to avoid repeating a word are generally ham-fisted and unnatural. I know there is a word for the act of not repeating a word, but I can't remember what it is.
Defined by Oxford Dictionaries Online as "The stylistic fault of studiedly finding different ways to denote the same thing in a piece of writing, merely to avoid repetition."
The word you may be looking for is Conduplicatio
A rhetorical term for the repetition of one or more words in successive clauses.
The repetition of a word in various places throughout a paragraph.
"The inherent vice of capitalism is the unequal sharing of blessings; the inherent virtue of socialism is the equal sharing of miseries."
"And the world said, 'Disarm, disclose, or face serious consequences'—and therefore, we worked with the world, we worked to make sure that Saddam Hussein heard the message of the world." - George W. Bush
Or, thinking of the inverse of Conduplicatio, Dissimilation may be usable.
- The act of making or becoming unlike.
While Dissimilation is usually used in phonetics, not grammar, it may be adaptable to function for this purpose.
According to grammar.about.com (for whatever that's worth), the term "monologophobia" was coined by New York Times editor Theodore M. Bernstein in 1965. That page defines the word as
A fear of using a word more than once in a single sentence or paragraph.
The Horror aequi principle is one term used in linguistics:
the horror aequi principle ... involves the widespread (and presumably universal) tendency to avoid the use of formally (near-)identical and (near-)adjacent grammatical elements or structures