This is partially why I keep my profile pretty baren. No display name, picture, bio, etc.
Edit: I don't usually do this but I'm too curious, why would someone downvote this? You want me to be more attention grabbing? Oh, never mind, they hit everyone.
That's not just YT. A lot of services and apps (e.g. amazon or xitter) you're logged into and share links from add parameters (stuff behind the questionmark) to the link that identify in the end who has shared it.
Try to shave off as much as possible from a shared link and test if it still works. To get a feel for what you can delete from the link, try to navigate to the destination (e.g. YT-video) inside a browser with which you're not logged into that service and which has preferrably cleared its history, cache etc. Then compare the link from that browser with the one from the browser you're logged in with.