You are looking for Michael Moorcock's Eternal Champion series. This is a large series of books that don't follow a single character but a kind of meta-character for which the series is named.
As summarized by Wikipedia:
The Eternal Champion, a Hero who exists in all dimensions, times and
worlds, is the one who is chosen by fate to fight for the Cosmic
Balance; however, he often does not know of his role, or, even worse,
he struggles against it, never to succeed. Since his role is to
intervene when either Law or Chaos have gained an excess of power, he
is always doomed to be surrounded by strife and destruction, although
he may go through long periods of relative quiet.
The name of the first title is Eternal Champion. Here's part of the plot summary (again, from Wikipedia) of this title:
The Eternal Champion is narrated by John Daker, an inhabitant of 20th
century Earth. At the beginning of the novel, his sleep is disturbed
by dreams of other worlds and a repeated name: Erekosë. After many
nights he understands that he is Erekosë and he finds the strength to
answer the call. He arrives in a world that is strange to John Daker
but somehow familiar to Erekosë (the narrator struggles to reconcile
these two viewpoints throughout the book). He is welcomed by the
ageing King Rigenos of Necranal and his daughter Iolinda, and receives
Erekosë's legendary sword Kanajana. The sword emits a deadly radiance
that quickly kills anyone who receives even a minor wound from it.
(Readers familiar with Elric will immediately recognise Kanajana as an
Avatar of Stormbringer by virtue of its dark color and magical
Rigenos explains to Erekosë that all of humanity is united in a
desperate fight against the inhuman Eldren, who have claimed the
southern continent Mernadin and are said to be seeking to expand their
empire. (The Eldren have some resemblance to elves as depicted in the
works of Tolkien and others, but the term is not used).