Yes, it is safe, we have been doing it for years. We prefer our tenants to make their rent payments in this manner. In fact, we prefer that they set up an automatic payment for the rent, either through their online banking or through their bank directly.
Apart from getting your rent on time, this method also has the added benefit of both parties having their own records of rent payments through their bank statements, in case there is a dispute about the rent sometime down the track.
Having a separate bank account just for the rent does make sense as well, it makes it easier for you to check if rent has come in, it makes it easier if you need to compare your statement without having to highlight all the rent payments amongst all other payments (you might not want to show your other incomes and spending habbitshabits to others), and you can withdrawlwithdraw the rents to your other account (which might offer higher interest) after it has come in, leaving a small balance most of the time in your rent account.