The way it is currently mapped appeals to my sense of logic, since it means we can follow the full length of Fetter Lane strictly sticking to ways named "Fetter Lane" (as it diverts onto that smaller side-road to the north)

But then again it wouldn't be at all shocking to find naming that is _not_ pleasingly logical!

I just walked along there and couldn't see any signs to clarify the name of this particular bit (which isn't really a surprise).