Instagram/Facebook is NOT going to do anything about the name. Just look at the history. Facebook launched an iOS app and called it "Paper." And guess what? There was a very popular app, which was called "Paper" too.

From recent cases I only remember Microsoft to change their mind in regards to their "Metro" OS. However, even in that case Microsoft decided to back off because "Metro" was a big retailer that sold Microsoft's products, so bad blood could cause bottom line to take a hit.