Who is Morwen?

[Tar-Palantir]

I was able to search this out, as I had not heard of Morwen either.

Per LOTR and Unfinished Tales, Morwen of Lossnarch was Theoden's mother, and kinswoman of Prince Imrahil of Dol Amroth. She was of high Numenorean descent. (This explains Aragorn's observation that Eomer is a kinsman from afar.)

Strictly speaking, Morwen must have been long dead by the time of the War of the Ring. It seems unlikely that the movie would have a flashback showing Theoden's youth long before the timeline of the War.

Although "Morwen" is a name foreign to the Rohirrim, it would be considered a name of honor, and so later generations may have used it.

Unfinished Tales also has the dramatic story of the Oath of Eorl on Elendil's tomb on top of Halifirien, and mentions that this Oath was renewed by Eomer to Aragorn, since Eorl had sworn only in the presence of the Steward, not the King.

It is plausible that this scene of Eomer's oath could be added to Return of the King, giving the characters something to do on the ride from Gondor to Rohan with Theoden's bier, besides getting saddle sore