The usual term for this is "single-sourcing", and it applies to much more than vendor selection in RFPs. You can single-source materials, vendors, locations, or anything else, and it's routinely done in legislation.
When a specification is written specifically for a single vendor, it's not called single-source; although the end-user probably advocated for single-source during negotiations with the procurement department. Not surprisingly, this is a constant source of friction for procurement departments. End-users almost always want to buy their preferred solution, and especially in IT. There are often good reasons, but I digress.
In some contexts, the single-source procurement strategy is simply not available; usually due to procurement law. This is when you most commonly see manipulation of specification. However, competing vendors can challenge the procurement in court through a procedure usually called a "bid protest". That's not exactly what's happening here, but it's similar.
1: The person who will ultimately use/implement the purchased goods/services.
2: Usually a separate department responsible for ensuring that goods/services are "responsibly" procured.
...this isn't accurate. Intentionally writing a specification that only one party can meet is in fact called single-sourcing.