Incy Wincy Spider

I was reciting Incy Wincy Spider yesterday, as one does, and I got to thinking:

Is Incy Wincy the spider's name? - as in "Incy Wincy, a spider, 43, was found climbing up a spout..."

or, is incy-wincy an adjective? - as in "An incy-wincy spider, climbing up a spout..."