Upvote:0
The authoritative source for the meaning of Spanish words is the dictionary of the Spanish Royal Academy. In its entry for representante here we find several possibilities but the most clearly relevant one is number 2.
So it is a masculine or feminine noun meaning "Person who represents someone not present, a body, or a community." The other definitions it gives are also about people not about companies. So one would deduce that they require the name of a person not the company.
Upvote:2
[From my comments]
A company cannot invite you. So probably it is a person from such company that invite you. Already with small companies, probably most of people never heard your name, and how many people on that company could explain why they invited you? So use a person name (with company role).
This is important, if they want to verify your data. The control officer should be able to contact a person who can confirm your application. Otherwise, the application could be delayed, or worse, it will deny the appeal.
BTW: ask that company to help you with appeal. They know a lot better how the administration work on Spain, and what it is to expect
Also this point is often overlooked. We tend to think that other countries works like our own country, and officer on that country tend to expect that people follow the correct procedures.