Thanks for everyone's thoughts. We generally have been calling it a "holding deposit" here in CA, and stating that it will be credited toward the first month's rent.
For CA, the Dept of Consumer Affairs has a section on it in their landlord tenant handbook:
HOLDING DEPOSIT
Sometimes, the tenant and the landlord
will agree that the tenant will rent the unit, but
the tenant cannot move in immediately. in this
situation, the landlord may ask the tenant for a
holding deposit. A holding deposit is a deposit
to hold the rental unit for a stated period of
time until the tenant pays the first month’s rent
and any security deposit. during this period, the
landlord agrees not to rent the unit to anyone
else. if the tenant changes his or her mind about
moving in, the landlord may keep at least some
of the holding deposit.
Ask the following questions before you pay a
holding deposit:
• Will the deposit be applied to the first month’s
rent? if so, ask the landlord for a deposit
receipt stating this. Applying the deposit to
the first month’s rent is a common practice.
Is any part of the holding deposit refundable
if you change your mind about renting? As
a general rule, if you change your mind, the
landlord can keep some—and perhaps all
—of your holding deposit. the amount that
the landlord can keep depends on the costs
that the landlord has incurred because you
changed your mind—for example, additional
advertising costs and lost rent.
You may also lose your deposit even if the
reason you can’t rent is not your fault—for
example, if you lose your job and cannot afford
the rental unit.
If you and the landlord agree that all or part of
the deposit will be refunded to you in the event
that you change your mind or can’t move in, make
sure that the written receipt clearly states your
agreement.
A holding deposit merely guarantees that the
landlord will not rent the unit to another person
for a stated period of time. the holding deposit
doesn’t give the tenant the right to move into
the rental unit. the tenant must first pay the
first month’s rent and all other required deposits
within the holding period. otherwise, the landlord
can rent the unit to another person and keep all
or part of the holding deposit.
Suppose that the landlord rents to somebody
else during the period for which you’ve paid a
holding deposit, and you are still willing and able
to move in. the landlord should, at a minimum,
return the entire holding deposit to you. You
may also want to talk with an attorney, legal
aid organization, tenant-landlord program, or
housing clinic about whether the landlord may be
responsible for other costs that you may incur
because of the loss of the rental unit.
If you give the landlord a holding deposit when
you submit the rental application, but the landlord
does not accept you as a tenant, the landlord
must return your entire holding deposit to you.