We would like to know if there is a single word to describe fear of change.
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I see neophobe has been suggested at least a couple of times, but I personally find this term a little clinical. There are many ways to describe someone resistant to change, depending on the cause for resistance.
In the negative sense, a fuddy-duddy, fogy, or mossback is someone, perhaps an older someone, with a dislike for recent developments in fashion, technology, or culture (and by implication is somewhat unfashionable, luddite, or philistine); they are set in their ways.
More positive, or at least neutral, words for those with a preference for the old ways include traditionalist or classicist; they might gently be dismissed as members of the old guard or old school who repeat the old line. Resistance to change that derives from moderation and caution makes someone conservative, reticent, or leery.
But if one clings to one idea and expresses intolerance for others, he becomes a die-hard or hidebound, and any synonyms for chauvinism, fearfulness, or intolerance may suffice. Those who not only resist change, but seek to reverse previous change, are reactionaries.
A square or stick-in-the-mud is resistant to anything unconventional; they have an establishment or bourgeois mentality. Fear of change due to small-mindedness is characteristic of insular, provincial, parochial, small-town, or pedestrian thinking.