If you don't wish to give your bank details to someone paying you via TransferWise, you can now nominate a primary account for the currency you want to receive.
You simply need to go to your 'Recipients' page from the menu at the top of the screen, where you'll see all your recipient accounts. If you haven't previously sent money to yourself in another currency, you can add your account by clicking 'Add new' next to 'My bank accounts'.
Once you've added your account, you can click the arrow next to 'Send money' in the account you want to nominate and you'll see the option to 'Mark as primary account to receive XXX' (This will be the relevant currency to that account, e.g. EUR, GBP, CHF etc). Once you select this, you'll then need to verify your email address.
You'll be sent a verification email, where you simply need to click a link to confirm this is your email. Once this is done, you can return to your 'Recipients' page and follow the above process again and this time you'll see this.
Once you see this - your account is nominated and you can give others your registered TransferWise email address instead of your bank details.
Please note that if you are sending from USD, you will not be able to choose to send a transfer to a Primary Account unless the address has also been entered.