Fortunately with OUD this is a very easy problem to solve. You simply change the system wide default size-limit to 1. This will prevent anonymous and any non-administrative users from returning the full list of registered databases. However, it is important to note this is not a recommended approach for general use because most directory service client applications return more than one result. In the case of TNS name resolution, that is the the only use case for normal clients.
With the default TNS configuration an anonymous search can list all registered databases:
$ ldapsearch -T -h tns1.example.com -p 1389 -b dc=example,dc=com -s sub 'orclNetDescString=*' dn
dn: cn=mydb1,ou=Databases,cn=OracleContext,DC=example,DC=com
dn: cn=mypdb1_tns1,ou=Databases,cn=OracleContext,DC=example,DC=com
dn: cn=mytestdb,cn=OracleContext,DC=example,DC=com
$ dsconfig -h tns1.example.com -X -p 4444 -D 'cn=Directory Manager' -j /u01/cfg/...pw --no-prompt set-global-configuration-prop --set size-limit:1
$ ldapsearch -T -h tns1.example.com -p 1389 -b dc=example,dc=com -s sub 'orclNetDescString=*' dn
dn: cn=mydb1,ou=Databases,cn=OracleContext,DC=example,DC=com
SEARCH operation failed
Result Code: 4 (Size Limit Exceeded)
Additional Information: This search operation has sent the maximum of 1 entries to the client
$ ldapsearch -T -h tns1.example.com -p 1389 -b dc=example,dc=com -s sub 'cn=mydb1' orclNetDescString
dn: cn=mydb1,ou=Databases,cn=OracleContext,DC=example,DC=com
orclNetDescString: (DESCRIPTION= (ADDRESS = (PROTOCOL = TCP)(HOST = tns1.example.com )(PORT = 1521))(CONNECT_DATA = (SERVICE_NAME = mydb1 )))
ldapsearch -T -h tns1.example.com -p 1389 --simplePageSize 1 -b dc=example,dc=com -s sub 'orclNetDescString=*' dn
SEARCH operation failed
Result Code: 50 (Insufficient Access Rights)
Additional Information: The request control with Object Identifier (OID) "1.2.840.113556.1.4.319" cannot be used due to insufficient access rights
$ ldapmodify -h tns1.example.com -Z -X -p 1636 -D "cn=Directory Manager" -j /u01/cfg/...pw <<EOF
dn: cn=tnsadmin,ou=TNSAdmins,cn=OracleContext
changetype: modify
add: ds-rlim-size-limit
ds-rlim-size-limit: 0
EOF
Blessings!