How do I set the default search for Finder to filenames which INCLUDE the search term (rather than just begin with it)? Yosemite
The Finder searches for word prefixes.

If you save your search as a Smart Folder and then inspect that using a text editor (e.g. TextMate) you will see the raw Spotlight query:

((kMDItemDisplayName = "foo*"cdw))


The "w" modifier tells Spotlight to search for words. The "*" wildcard at the end of the search string makes Spotlight search for word prefixes. It will match names that contain a word beginning with "foo".

That matches all of your examples but one. "foo" comes at the start of the file name, after a space or punctuation or is capitalized. The exception is "snafoos" where "foo" is just a sequence of letters in the middle of the word.

You could change the query in the smart folder to:

((kMDItemDisplayName = "*foo*"cd))


Or click the "+" button below the search field in Finder and add a "name" "contains" "foo" criterion.

Or use mdfind in Terminal:

mdfind -onlyin . '((kMDItemDisplayName = "*foo*"cd))'


Or use HoudahSpot (of which I am the developer) to get more control over your search.