Since you mentioned IBJJF rules, this is in the current rule book:
https://ibjjf.com/wp-content/uploads/2019/05/IBJJF_Rules_Book_v5.1.1_en-US.pdfcurrent rule book (v5.1.1).
See "Article 5: Registration", page 43.
5.8 The athlete may only compete as the belt they are registered under with the IBJJF (or its affiliates). If the athlete is promoted by his/her teacher before the minimum time spent in the previous belt requirement is met or minimum age, he/she cannot compete in this current belt nor the previous one.
5.9 Once an athlete’s gradation occurs, he can not compete in his previous belt anymore. If he gets promoted during a competition after his division is done, he will be forbidden from competing in the open class.
So the answer is that you have to be registered under the IBJJF with that rank, and there's a certification process to make sure you really qualify as having that rank.
Hope that helps.