Many thanks to everyone for advice, information and ideas.

But the thing that I can’t get my head round, is this...
I’m imagining myself in the 1940s and I’m arranging a funeral and putting a notice in the paper.
If ‘Cowpen Cemetery’ and ‘Blyth Cemetery’ are one and the same, and there is no other cemetery, then it doesn’t matter how I refer to it in the newsaper announcement.
But if my relative is going to be buried in Blyth Links Cemetery, I need to make sure the mourners go there, and not to Cowpen.
I know the British Newspaper Archive doesn’t always return search results that we know must exist, but when I type in ‘Blyth Links Cemetery’ there are only 5 results – one from the 1890s (and the article wasn’t about a funeral) and 4 from the 1980s and 90s, where funeral notices specified Blyth Links. Searching just for ‘Blyth Links’ just returns results about the general area/seafront and ‘seaside cemetery’ returns no results for the North of England.
So during the preceding decades, surely there must have been funeral announcements directing mourners to Blyth Links... but I can't find any! Unless, of course, it was referred to as something else entirely

If that makes sense...!