Fame can come from being born in a famous family or from achievement or accident. A poet may achieve fame through education, from being born in the right place or having a timely message. It may come through charisma or Intelligence or from a knack with words. Homer was among the most famous poets of his day and in great demand among wealthy patrons to recite his extensive repertoire. Most poets who are included in school literature textbooks were famous at one time, although that fame was often fleeting.
Some poets rise and fall in their acclaim over time.
If you were to check out a book of the best known writers of each decade of the twentieth century, you would find that some of the lesser lights of earlier decades rose in esteem in the literary world and some of the believed greatest lost their appeal with the passage of time. This is even more dramatically demonstrated if you find an anthology from each century since the invention of the printing press. I have a book at my desk of the one hundred best American poems from 1905. There are many recognizable names but also many I have never heard. They know more Than they have ever understood, And speak at length About what they have never Known in depth.