yeah, even if it was possible to be anonymous, it wouldn't be safe. it is good to be verified while investing, especially when you use reliable and trustworthy cryptocurrency exchange, there is nothing to worry about, that they have got your data
You still need to worry since they got your data, how is not that worrying? But this is not what Bitcoin made valuable, the reason here is that Bitcoin is the first crypto currency, the most expensive and with a lot of users and its volatility, obviously a lot of people would risk their money to invest on it.