Yes, when signed in to a google account at least (if you belong to gmail or youtube etc you are probably signed in whenever you use youtube).

If you want to switch this off, then as of writing this, you go to https://myaccount.google.com/act... which lets you pause youtube search history (using the blue slider) and also Web and App activity to do the same for google searches.

When signed out of your google account, they personalize google search results using anonymous cookies, you can go to https://www.google.co.uk/history...

though I’m not sure if that applies to youtube searches or only google searches.

Google searches are also customized based on your country and your location within a country, even down to ip address. I don’t know any way to disable that. Youtube is also customized at least at the country level, and they give instructions for changing this here: Change language or content location settings but Youtube frequently change their interface, the arrangement of the menus etc, and I can’t seem to find where it is.