Facebook and YouTube offer a limited level of compatibility. YouTube links on the social network automatically display a thumbnail, for example, but you can't tag your Facebook friends from the YouTube interface. To tag people in YouTube videos on Facebook, you need to create a Facebook update linking to the YouTube video, and then tag the update with the names of your friends. Alternatively, if you have access to the original video, you could upload it directly to Facebook and not utilise YouTube at all.
Open YouTube and browse to the video you want to use. Click "Share" and then copy the URL text in the "Share this video" box.
Log in to Facebook and click inside the "Update Status" box to begin creating the link. Alternatively you can browse to a friend's Timeline if you'd prefer to post the link on someone else's Facebook profile.
Paste in the URL you copied earlier and a thumbnail and description will appear. Tick the "No thumbnail" box if you'd rather hide the thumbnail, or click the light blue cross to the right to remove the thumbnail and the description.
Add any text required before or after the link you've pasted. Be careful not to alter any part of the URL itself.
Click the "Tag" icon and type out the names of the friends you want to tag. When the correct name appears, select it and begin typing the next one.
Use the audience selector drop-down to control the audience for your post and then click "Post" to publish it. The friends you've tagged will receive notifications of the post and other friends may see it in their news feed.
The tags you add to the Facebook update are not transferred back to YouTube, and there's no indication on the YouTube video page that anyone has been tagged. The ability to tag Facebook friends on YouTube directly is not currently supported.
By default, content tagged with the name of one of your friends can be seen by that person's friends as well. This behaviour can be altered from Facebook's privacy settings, but only for your own account, not the accounts of others.