I know what
Eomer means with the names and introducing characters. When my niece first watched the movies she thought Eomer was Boromir's brother (I guess they look kind of a like), and then I said it was Eomer. She's like who, and I said watch.
My favorite part, and probably one of my favorite lines of this sequence is Eomer telling Grima:
"Too long have you watched my sister, too long have you haunted her steps." Directly from the books, but Gandalf is given this line in the books, and I like the change over to Eomer (though it be minor I think Jackson did the right thing). No disrespect to Tolkien, but I think the line suits Eomer, being Eowyn's brother, much better than some random old guy that pops in once in a while.
I perhaps will have more, as I'm trying to catch up on the time I've missed but it's late.