For the people who want him to reveal his identity... do you not understand the implications of a prince from a large nation being the slave of a small nation? Do you think they're going to be like "oh sorry, we'll free you from being a slave now"???
Besides, his main goal is researching the resurrection magic, something he didn't tell anyone about even in his past life. And, like he said, if his owners know that he knows OP magic in addition to being really strong martially... well you'd have to be really stupid to not know that won't go well for him.