What is the Old English heroic poem surviving in a single copy dated around the year 1000 featuring its eponymous 6th century warrior from Geatland in Sweden?

That would be Beowulf.

Beowulf is an Old English epic poem which consists of 3,182 alliterative long lines.
It is, as far as we know so far, the oldest surviving long poem in Old English. It is also regarded as one of the most important works in Old English literature.