You get a replication conflict.
One of the accounts will get to keep the desired name, and the other will be automatically renamed to something else to resolve the conflict.
This very example is actually used here, and the relevant parts are pasted below.
Consider the example of the jsmith user object in the contoso.com
domain. An administrator on DC1 changes jsmith's description to
"Marketing." Nearly simultaneously, an administrator on DC3 changes
the same user's description to "Sales and Marketing." At this point,
DC1's and DC3's information about jsmith's description attribute
compare as shown in Figure 9.
If DC2 receives both of these changes simultaneously, it will clearly
need to determine which one is the "winning" change. The order of
tiebreakers for conflict resolution is as follows:
The modification that has the higher versionID will be accepted as the
"winning" change; the "losing" change will be overwritten. In this
case, the versionID is 2 for both records, so we need to move onto the
second tiebreaker.
If both records have the same versionID, the change that has the later
timestamp will be accepted as the winning change; the losing change
will be overwritten. In this case, the timestamp from DC3's
originating write is later, so jsmith's description will be set to
"Sales and Marketing." In the rare instance when both the versionID
and timestamp are identical, we need a third and definitive
tiebreaker:
If both records have the same versionID and timestamp, whichever write
was originated by the DC with the lower-numbered GUID will win; the
write from the higher-numbered GUID will be overwritten. So if DC1's
GUID is 1234567890 and DC3's GUID is 2345678901, the originating write
from DC1 would win if both the versionID and timestamp were identical.
You are probably thinking, "Wouldn't it make more sense to have the
timestamp be the first tie-breaker?" This isn't as cut-and-dried as
you might think. If timestamp were the primary tie-breaker in Active
Directory conflict resolution, the only thing that a malicious
administrator would need to do to propagate his or her changes would
be to set back the clock on one particular DC so that it would always
win by way of timestamps.
Resolving Conflicting Object Creation
In cases where two objects are created with the same name, Active Directory will use the same three
tie-breakers described in the previous section to determine which one
is the "winning" object. Unlike the previous section, however, the
"losing" object doesn't get overwritten. Instead, the losing object is
renamed using the characters CNF (for conflict object), followed by a
colon and the GUID of the "losing" object. This allows administrators
to more methodically determine which object should be retained and
which should be deleted.