Thank you, everyone, for the responses. While I did get the answer I was looking for(though definitely not the one I wanted), I feel some things need clarified.
These are not telemarketers. They are bill collectors looking for a certain person. They do NOT have the right to continue calling me at all hours/at work after I have asked them to stop even if they were telemarketers. I wish they were sales calls, because then my rights would be much broader. I could ask them for a company name and expect to get it. Adding this number to the do not call listing will help keep me from getting unwanted sales calls in the future, but it is going to do nothing to stop the people from the collection agencies from calling looking for the previous owner of the phone number. The only thing that will do that would be to force their hand in revealing a phone number by blocking all attempts at getting through on a restricted line. Apparently Verizon is more concerned about the privacy of anyone and everyone but their customers. This is a feature that needs adding to Verizon.
So again, thanks to those that answered. Maybe someday Verizon will get with it and realize that the needs of their customers who are paying them should come before the needs of shady debt collectors who refuse to understand that the woman they are after is no longer at this number.