I also worked in collections for nearly a decade. More over I worked in skip tracing helping repossess cars. If you send a cease and desist letter all that will happen is they will remove the numbers from your VALID account that they can easily find, and you risk not being notified if something is wrong with your real account.
Skip tracers get accounts with no contact information and try to locate the debtor. I would bet $100 they are trying to "skip trace" this other woman of the same name and in doing so are calling numbers listed to people of the same name. It could be more sophisticated then that - they may have this number coming up in Lexis Nexis, Fast Data, or some other data tool. You need to answer when a skip tracer calls and talk to a manager. Document who you're speaking to and get them to note the account - her account - not to call you. The good news is they have NOT put your number on her account, if they had other reps would be able too pull the account by your number.
It's a pain, and very annoying. I've gotten calls from people looking for my ex husbands new wife. The skip tracing tools professionals use try to generate leads and link together "possible" family, as well as the skip tracers themselves doing some digging and trying to make educated guesses.
What I would do, personally, is document the calls date and time. Get the womans full name (you mentioned knowing her middle initial) and speak to a rep when they call... document the reps name and get as much info about the account that is NOT yours. I would send a certified letter, keep a copy and the receipt that someone signed for it. If the calls continue then I would file a BBB complaint about the calls for the other womans account. Include EVERY step that you've already taken -- who you spoke with, the certified letter, etc. Most companies take BBB complaints very seriously and will take the extra steps to get the complaint resolved.
Good luck.