What is the ruling on the prize that the questioner won in a competition by mistake, given that he used his friend's name in the account that won two prizes? Is it permissible or forbidden?

If the competition organizer allows an individual to enter with more than one account, there is no harm in taking both prizes. However, if they do not allow it, then you are not entitled to the prize you received in your friend's name, and you must return it.