I hope you have a Twitter account. Did you notice the search button on top of the Twitter web page, didn't you?

Just copy the YouTube video ID (not the YouTube video URL) from your browser's address bar and, paste the same into the Twitter Search field. You will get at least a few tweets mentioning the video. Sometimes, these tweets contain the name of the song used in the video.

As you can see the video ID in above screenshot, that last random alphabets and numeric is call video ID on YouTube. The main reason behind picking only the YouTube video ID and not the whole YouTube video URL is that same video can have many different links as you may know YouTube has many publishers for the same video. But the video ID is always the same except in few shortURL services.