Are you a Master's student?
It's entirely up up to you - I don't think this is something we can really help you with. It sounds like you're nervous about sharing your work with a wider audience, but I'm sure you can ask for it to be anonymised. I think I can understand where you're coming from - I'd be worried about people plagiarising my work or stealing my ideas but there are academic tools that can be used these days to sniff out plagiarism, and if it's an essay they use in teaching at least they'll be more aware of any academic dishonesty. I'd be chuffed if my sup wanted to share my work (can't ever see that happening!) so well done you, your writing must be excellent! Sorry if that's a muddled reply, I'm in the middle of writing up at the moment and my brain is fried!