You can insert two OP_HASH160 after the OP_DUP and then push the hash of your pubKeyHash. Nobody can tell the recipient address this way.
Example:
OP_DUP OP_HASH160 OP_HASH160 double_double_hash OP_EQUALVERIFY OP_CHECKSIG
Where
double_double_hash = RIPEMD160(SHA256(RIPEMD160(SHA256(pubKey))))