To add to Quilted Dove's explanation on finches -- I had a pair once. She forgot to add how prolific they are -- once I put that little nesting basket in their cage (because I was dumb and thought it was cute), the female started laying eggs like crazy. They would hatch, daddy would literally push them out of the nest when he thought they were ready, then 6 more eggs would appear. Every one I knew soon had finches, every pet store became well stocked to the point they would lock their doors when they saw me coming. So you might want to add "fertility" and "stamina" to their symbolism.
I like "Thimble and Finch", or "Quilted Nest", "Patchwork and Feathers", "Feathers and Fabric Craft" ... nah, I keep going back to "Thimble and Finch" -- that was a good one.