The official answer in the present body of knowledge, as expressed by ChaGPT is below. Anyhow, I strongly believe Steve's recount about Bakhtananda and his unofficial reports.
In other ways, SRF does not endorse things which Yogananda himself, or presidents, have affirmed. Which does not eliminate the fact that he might have been.
William the conqueror is another very likely incarnation, Durga Ma in her book wrote about that.
According to the beliefs of the spiritual organization founded by Yogananda, the Self-Realization Fellowship (SRF), Yogananda did not claim to be the reincarnation of Shakespeare. In fact, the SRF does not endorse the belief that any particular person is the reincarnation of another specific individual.
Yogananda did teach about the concept of reincarnation and the idea that souls can take on different physical bodies in different lifetimes. However, he emphasized that the ultimate goal of spiritual practice was not to focus on past lives or future incarnations, but rather to achieve self-realization and oneness with the divine.
It's worth noting that the idea that Yogananda was the reincarnation of Shakespeare is a popular myth or rumor that has circulated in some spiritual circles. However, there is no evidence to support this claim, and it is not endorsed by Yogananda's teachings or the SRF.