I'm afraid Eikon .NET SDK does not provide an interface for news. The most you can do is to subscribe to the RIC NFCP_UBMS, which provides the live stream of all news headlines you can receive. However, there's no backfill of headlines through this RIC. I.e. you can only retrieve the headlines that are published after you start the subscription. And no filtering capability is provided. You'd have to implement filtering yourself based on the content of a headline update.
Same way you subscribe to any other RIC. It may be helpful to look at this RIC in a Quote app in Eikon application to see the list of fields and how the content is updated. Looking at this RIC in a Quote app should give you a pretty good idea whether it's of any use for your purposes.