I have no idea of other VRS than Sorenson. I wouldn't worry too much, and won't lose sleep over this. Many of you may not realize this, like any calling center, they process thousands of calls each week making it very difficult for them to remember details of every calls. I received too many calls back then when I work for VRS, I always ask for address verification, guess what? I can't even remember single of them! Even customers names too! It was really difficult for me to remember anything that I have done at work. Sometimes customer recalled me and asked me if I remember them, it was real embarrassed for me that I can't recall them. It applies to terp too, they have to process tons of calls, there is no way they could remember. Rest assure that they have to adhere very, I mean very strict policy and I believe (Due to FCC regulations) that they apply on the rest of relay industry that they CANNOT bring anything to their work except themselves. They can't bring in cell phone, notepad, laptop, paper, pen, etc. If they were caught bringing them to their work, it is their ground for termination (Most cases instant termination). No relay employees can afford this risk because they will be blacklist by FCC and barred from working with any relay companies. No relay companies can afford these risks because FCC is watching them like Hawk. Also, some of you think terp might take a break from work after your call anytime, it does not happen that way. Terps are randomly select for break by supervisors, they can't leave their work until supervisor give them green light making this difficult for them to cheat the system.
Keep in mind, jot down terp ID that you see from screen not from the terp's hands. They all know that their ID is being displayed on the screen for Deaf customers to see, which is good thing because they know their ID is being recorded.
I personally have used VRS since 2003, and I have relay my SSN and other sensitive information with them and have not had single issue with them, including ID thieves.