I can't see the texture in that photo -- need something much closer. In the meanwhile, here's an image search on "drywall textures". Find the one(s) that are closest to what you have and then search for possible methods to create it.

Do something different...cover it with wood tambour and extend the wood down part of the hall.

Tambour comes in panels , found in any home improvement store. You could stain or paint it the wall color.

Thanks for the suggestions. We ended up skimcoating it entirely! It wasn't my preference but it looks great.