No. In fact, there are good reasons to maybe not put her name of the lease. Federal law (SCRA) allows a military service member to break a lease at any time with no penalty if they receive PCS/mob orders to another location for >179 days. Some landlords and mgmt companies are dicks and may try to argue that she isn’t eligible to get out of her lease obligation early (severability of parties). You will receive orders after OCS and you‘ll want that flexibility.
I believe the only thing you need to receive BAH is to enroll her in DEERS and have an updated, verified Pg 2 of your dependent info. If you’re non prior service, work with your recruiter or any points of contact at Newport your recruiter gave you.