In general I don't think it's necessary for people to adopt an anglicised (English style) name. Many English speaking countries and communities are now very multi-cultural. Partly because lots of people who have foreign origins live in many English speaking countries, and partly because we consume media (films, TV, internet, etc) from all over the world. Therefore we are familiar with non English names, and most people are very, very flexible about trying to pronounce foreign names (and maybe the very small minority who don't like to pronounce foreign names are not the sort of people that you should be friends with anyway?) .
On the other hand it's true that some names are very difficult for us if they contain sounds that don't exist in English.
In your specific case I don't think it would be difficult for most English speakers to pronounce an approximate version of your name "Yan" ...we might not be sure if we should say "Mai" as 'may' or 'mi'.... but it's not a big problem.
If you want to use Aurora as a sort of nickname, then I think that's very suitable... but be prepared for lots of people who then excitedly ask you how you got that name (questions like "Did your parents choose it?") ... and then you will probably still have to explain that your real name is Yan Mai :-)