In Stratum protocol, whether the miners know the mining address?
Yes, it is possible. The coinbase outputs are embedded in coinbase2.

E.g. for a regular 1-output pay-to-pubkey-hash coinbase tx it contains the pubkey hash which can redeem the coins.

Check the stratum official documentation. It has a real-world example which generated raw block 000000002076870fe65a2b6eeed84fa892c0db924f1482243a6247d931dcab32.

The raw transaction output[0] looks like this:

{
  "value":"50.00000000",
  "scriptPubKey":"OP_DUP OP_HASH160 d23fcdf86f7e756a64a7a9688ef9903327048ed9 OP_EQUALVERIFY OP_CHECKSIG"
}


Or, in hex, 00f2052a010000001976a914d23fcdf86f7e756a64a7a9688ef9903327048ed988ac.

The miner gets this parameters from stratum:

"params": [
  /* job id    */ "bf",
  /* prevhash  */ "4d16b6f85af6e2198f44ae2a6de67f78487ae5611b77c6c0440b921e00000000",
  /* coinbase1 */ "01000000010000000000000000000000000000000000000000000000000000000000000000ffffffff20020862062f503253482f04b8864e5008",
  /* coinbase2 */ "072f736c7573682f000000000100f2052a010000001976a914d23fcdf86f7e756a64a7a9688ef9903327048ed988ac00000000",
  /* omitted, not relevant */
]


Notice coinbase2 contains the hex of the block output, including d23fcdf86f7e756a64a7a9688ef9903327048ed9, i.e. the pubkey hash (which you can derive the address from).