A Boggart is an established creature from folklore.
Boggart is one of numerous related terms used in English folklore for either a household spirit or a malevolent genius loci inhabiting fields, marshes or other topographical features.
As we know, JKR took many of the creatures in the book, and references, from existing mythology. (Like Fluffy -he's almost 100% for sure based off of Cerberus, from Greek mythology. Hagrid gets him from 'a Greek chap'.)
So, it's safe to assume that she based the name of the Boggart on... boggarts.
The boggarts of J. K. Rowling's Harry Potter series are unlike most boggarts of British folklore. Their closest parallel, in being able to change shape at will, is probably to be found in a reference to a Lancashire boggart in the book Lancashire Folklore of 1867.
To put it clearly: It looks as though she took this the way she did most other things: She took the name it from existing Mythology/Folklore. However, it looks like she did not take the attributes of the boggart from existing mythology - or anything - but made up her own creature with a name from existing folklore.
According to @CreationEdge, Rowling never read that much scifi, and can't say that anything was inspired by what she read. She says as much:
THE question you are most frequently asked as an author is: "Where do you get your ideas from?" I find it very frustrating because, speaking personally, I haven't got the faintest idea where my ideas come from, or how my imagination works. I'm just grateful that it does, because it gives me more entertainment than it gives anyone else.