Unfortunately, there is currently no ability in Spotlight to search partial filenames. For instance, in the file: Janeplayingwithjack.jpg we can type any of the beginning letters of the filename, like "Janeplaying", but we cannot search with any of the characters in the middle or end of the file name, like "playingwithjack.jpg". There are times when you can only remember part of a filename, or you have a set of files with particular numbers or letters grouped with different titles before the end of the filename, or many other examples when this feature would be very handy.
Although you cannot find this in the Spotlight menu, you can do partial filename searches in Finder. Here's how to do it:
Type Command + F
Search "This Mac", and choose "File Name". Then choose to search by "KIND", then select what type of file it is you want to search.
Now, when you type partial filenames like "withjack.jpg", it will display the file "Janeplayingwithjack.jpg" along with any other files containing "withjack.jpg" in the filename.