Hi!
In my experience, when you make a purchase that will meet the threshold for VAT refund, they provide you with the necessary form from the store. I have received them from Global Blue as well as another company (I do not recall the name). They will generally ask for your passport during the purchase process and enter the information in the system. We have exited through FCO back to the US. One time we used the kiosks post-security and, on our more recent trip, we used the offices pre-security. There was a line as we were there just as they opened at 6 am, but the lines moved quickly. In that case, we had forms for two companies so it was much more convenient to use the offices since they were all together.
I have never registered in advance and do not see a reason to do so. If I decide to purchase something, I don’t want to worry about which VAT refund company the store uses.
One tip if deciding between the office versus the kiosk for your refund, we did learn they will pay you in cash (minus a small fee) should you prefer not to wait for a credit card refund. Unsure if that matters to you, but something we learned.
Have a wonderful time!