How do I make this information private on my Google account?

I've viewed my Google account as other people would see it, and there's a piece of information I want to make private but I can't work out how to.

I don't want people to have a link to my Youtube account (I've attached an image below so you can see what I mean). I can make every other option private and only viewable by me, but can't figure out how to make the link to my Youtube account private.

I've only just realised that people can click on my profile name when I send them an email, and with a few clicks, can view all the Youtube videos I have favourited and all the comments I write on Youtube. I've been emailing important people like employers and I don't them to view this information.