I'm not 100% sure if youtube minds. Someone from youtube actually put it on one of their videos (a button for it), and then said youtube community department were having fun and spreading it around

We don't use a 3rd party queueing software ^_^.

Maybe giftube.com or yougif.com?

I'd register those but keep what you currently have for now. Being able to say "put the word gif in front of any youtube url" is just great for user experience.

We will give you a free premium listing on BootName.com if you want community support to find a name.

My (unsolicited) layman's take:

Someone from youtube != Google's legal department, which makes this situation both awesome and sad. If Google wishes to maintain their ownership of the youtube trademark, legally they must enforce their ownership of it (which means either granting you a license, or sending you a C&D). That said, I'd search around for trademark licensing info - they may have an existing license which covers this use.

In the mean time you may be able to protect yourself a little by adding some text that says that YouTube is a legally registered trademark of Google, Inc., and this site is not affiliated with Google in any way.

I am not a lawyer, but it seems one could easily argue that an "idiot in a hurry" might confuse this for youtube. Which is sort of what the threshold is for this sort of thing nowadays. So, yea, start thinking about a domain that doesn't include youtube

Do you have plans to monetize it? How are you paying for the hosting.