Can the BR200 block websites by name

Yes and No. 

Yes, it can block HTTP site/domain. 

No, it can't block HTTPS site/domain. 

The "Site/keyword blocking" is a legacy function that is applied to HTTP traffic only. 

Thank you.

Leaving everything alone what's in the fine BR200 User Manual p.54 ff. "Specify keywords and domains to block Internet sites" what certainly works (except where it says "Specify the domain suffix (for example, .edu or .gov) if you want to allow only sites with domain suffixes such as .edu or .gov." which should read "Specify the domain suffix (for example, .edu or .gov) if you want to deny
sites with domain suffixes such as .edu or .gov." ... This would essentially answer your question.

When we would do some brainstorming here ... : How should this work on https, and then even if it would be redesigned to capture DNS instead of HTTP requests for example, in a world of end-to-end encryped https sessions, and then again on secured DNS? 

Hey, it's a nice little router, performing well, which can be Insight managed, for a -very- attractive price.

This feature however can't work as of now. Probably, we might see the coming-up Netgear SPC on these devices one day.