Is it permissible for me to keep the money gained by a person who bought my stolen account, which reached me by mistake in my name, as compensation for the damages I incurred from the disruption of my work, the destruction of my account, and the loss of an opportunity to earn a livelihood?

If the mentioned amount is in exchange for publishing advertisements on your usurped website, then it is rightfully yours because it is a growth from it, whether this growth is connected or disconnected, and whether it is generated from the origin or not. This is by agreement among the jurists regarding usurpation. You are also permitted to demand compensation for damages and to escalate the matter to the competent authorities.