All of which will pass through Farringdon, though. And vice versa,
every
train which passes through Farringdon will be on the Thameslink route.

Makes no difference, the name "Thameslink" refers to Brighton / Sutton
to
Bedford.

Er, what? That's what it refers to now, sure. When trains are running from
King's Lynn to Guildford or whatever, it'll refer to those too.

I would argue that from the travelling public's point of view, it won't
refer to those services at all. Since the name is not advertised to the
general public much (if at all), and the Train Operating Company are called
Capital Connect, I suspect the new combined service will become known as
Capital Connect. The official name of the line in the middle of it all won't
be heavily used, and so shouldn't be used for station directional signage,
after all LU don't sign "West Coast Mainline" anywhere.

National Rail or First Capital Connect is perfectly sufficient for signage,
and as it happens, I prefer the former.

Best Wishes,
LEWIS