Why do cookies have my name in them, and do the sites I visit see that?

In IE, click on Tools, then Internet Options, then the General tab, and in the "Browsing History" section click on Settings. Once there, click on View Files and you'll get a window much like this:

(You may need to re-sort, or scroll the list to see cookies, as other temporary files are stored there as well.)

As you can see, my cookies appear to include my name.

But also notice what you're looking at: a listing of files. In fact, my name is included only on the filename that contains the cookie. When the browser picks up the cookie and sends it on to whatever site is appropriate to send it to, the file name is not part of what's sent. Only the contents of the file containing the cookie is sent.

Where'd the name come from? That's your Windows login name. I happen to login as as LeoN (a holdover from my days at Microsoft where my login name was also "leon"), so that's the name that IE pre-pends to the cookie filename to identify it.

I'm actually not aware of a way to change it. You could create a new Windows login account, I suppose, and start over, but that seems rather extreme.

But as to the underlying concern: this is not something that the sites you visit ever see. It's simply a part of Internet Explorer's internal housekeeping. And in fact if you look at cookies stored by another browser, such as Firefox, you'll find that they're stored - and named - in a completely different way.