I’m a rank amateur, but I would say the opposite. If I were doing it, I would go out of my way to sign different names.
My wild guess is that this might be the work of ACORN or some such (or similar organization that employs uneducated people). They distribute a form letter and ask people to get it published wherever they can.
The sample letter had “Ellie Light.” Rather than substitute their own name or those of the Dallas Cowboys (you may recall an ACORN employee submitting fake voter registrations with the all the names of the Dallas Cowboys), they just leave it as “Ellie Light.”
If they leave it as “Ellie Light” then a coordinated effort is easier for the bosses to track.
any editor worth his/her salt will verify the name and address before printing.
Heck, I'm now retired from the business - kept my column tho' for many years before hanging that up too - and my editor will still call me and verify if I send a LTE.
Mostly, they will verify by phone book or registry to match name and address. but they don not just print, willy nilly - to avoid spam. They won't print from "anonymous" either.
If they printed without verification, they'd have to have separate mail sacks just to drag in the letters that people, who could hide behind anonymity, would send.