I'm not a historian, nor would I claim to be one, but I've seen a lot of people say that it was Laplace who formalized the theorem:
$$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$
Why don't we call it "Laplace's Theorem"?
Is there a technical or serious reason for continuing to give Bayes the credit?
I don't mean to be obstinate in asking this question, I'm honestly curious if there is a technical or serious answer to the question outside "Bayes was the first to come to the idea".
Thomas Bayes died in 1761, and his "Bayes Theorem" was published in the Philosophical Transactions of the Royal Society of London in 1763 after his death.
Indeed, Laplace first wrote down the general formula, but it was Thomas Bayes who first derived the special case of Laplace's general formula. One of the reasons why it is called Bayes Theorem might be that Laplace genuinely acknowledged Bayes's important contribution.
Here is what Laplace wrote:
"Bayes, in the Transactions Philosophiques of the Year 1763, sought directly the probability that the possibilities indicated by past experiences are comprised within given limits; and he has arrived at this in a refined and very ingenious manner, although a little perplexing."
Information from Bayes, Laplace and Bayes’ Theorem