When it comes to the usage of existing names in your product I always advice caution. When it comes to linking a game to a site the notice is all fine and even necessary, like an on-line trophy system, which itch.io does not have, but a similar game site does. Then noting the name of the site is just vital.
When it comes to your game containing a name, like in this case itch.io, I would actually advise against it. First of all the copyright issues are likely what is not in the way. The way I estimate the admins now they may not even mind. But what if itch.io would ever get sold? The current staff members are only human after all and won't level forever and you never know the stance of future owners. And this also brings you to another position. What if itch.io would ever break your trust. Seems silly to say here on the itch.io forums, but I do speak out of experience that websites may sometimes take a very very nasty turn you can never agree with. Many companies in general I used to speak highly of are now on my personal blacklist. If that would ever happen in the future the name is already in your game, and it can be one hell of a job to remove it all. That alone is reason enough to avoid it.
Of course, it is always your choice, and regardless if the itch.io staff allows it or not, I personally recommend against it.