The short answer is yes! The ATO must be able to confirm your identity. The way in which this is usually achieved is by checking your supplied details against your personal Tax File Number (TFN).
If you do not wish to provide your TFN in the application you must be prepared for your application to either be rejected at first instance or to channel through to the ATO's manual review system. This is a process which can take up to 28 days, during which time you will be contacted by an ATO representative.
In most cases the ATO will either insist that you submit your TFN or in the event that you don't have one, they will recommend that you apply for a TFN.
Another consideration is the personal details you have registered with the ATO. For most Australians, a TFN was obtained when they first began employment, often some years ago. If during this time you have undergone a name change, perhaps due to marriage, it is essential that you advise the ATO of this prior to submitting your ABN application.Should you not, again your application will be delayed. This applies to any identification information that may have changed.