On the one hand, Shakespeare's writings demonstrate a high level of ambition and craftsmanship, suggesting that he may have desired recognition and praise for his work. He took great care in constructing his plays, often revising them multiple times, and he had a deep understanding of human nature and the dynamics of power. Additionally, Shakespeare was aware of the potential of the theater as a medium for conveying profound messages and engaging audiences, suggesting that he may have wanted to reach a wide audience with his work.
On the other hand, Shakespeare's contemporaries did not always appreciate his work to the extent that he may have hoped. During his lifetime, he was primarily known as an actor and a playwright for the popular stage, rather than as a literary figure. It was not until after his death that his works began to be canonized and considered as great literature.
Moreover, Shakespeare did not seek publication of his plays during his lifetime, and some of his works were published posthumously or without his authorization. This may indicate that he was not overly concerned with preserving his reputation or ensuring his long-term fame.
Overall, it is possible that Shakespeare had some degree of desire for fame and recognition, but his motivations were likely complex and multifaceted. While he certainly possessed the talent and ambition to achieve renown, he may also have had other priorities, such as earning a living, pleasing his audiences, or expressing his creativity, that took precedence over the pursuit of fame alone.