xv pronounced as the fifteenth here?

No, i don't think so. I'd say it simply reads as fifteen, meaning that it is document number 15 in that codex. Codex is used by scholars to designate an ancient text. If the sheets of the text are not bound together in the form of a book, or if they are in the form of a scroll, it is necessary to number them in order to preserve the proper order. I believe that that is what is going on here.

Thanks

Agree with Setanta. The xv here is similar to a page number in a book. So -- fifteen, not fifteenth.

But Cotton Vitellius A. sounds like a man's name.

So what?

Since you seem to be stuudying the hoary old epic Beowulf as we see from another thread, it seems you are referring to the original manuscript which is known as Cotten Vitelius A. xv. This is strictly from memory but, if memory serves, the name Cotton Vitelius does not actually refer to a man but, rather, to a 'bust' (i.e. statue) of a man named Cotton Vitelius. The manuscript was discovered in a poorly-catalgued library under this statue and was, thus, identified by the man's name, the shelf on which the codex rested and the sheaf or page number. Again, this is from memory, but it's easy enoughto look up in Vikipedia probably.