There’s a reason I asked the question I asked earlier. “Yellow Flash” is more of a nickname tied to Minato’s exceptional speed, rather than his position or status. The nickname wasn’t about his rank; it was about speed and combat prowess and that did not change when he became the Hokage.
For instance, A day, or even a second, before Minato became Hokage, he was still a Jonin, and people would have recognized him as the “Yellow Flash” even as a Jonin who was about to become the Hokage, after Minato became Hokage, the nickname wouldn’t suddenly disappear because It had always been a recognition of his skill in battle, not his official position. Thus, even after he became Hokage, enemies who feared him wouldn’t stop associating him with the “Yellow Flash.” For example, if Hokage Minato were to step onto a battlefield, his enemies would still be terrified, saying, “Run, everyone, the Yellow Flash is here!” The name stuck because of his speed and reputation, not his title, similar to the Legendary Sanin, god of shinobi Etc.