In the log I see things like:

    2017-09-13 03:54:33 init message: Rescanning...
    2017-09-13 03:54:33 Rescanning last 68616 blocks (from block 416339)...
    2017-09-13 03:54:40 AddToWallet xxxxx  update
    2017-09-13 03:55:33 Still rescanning. At block 418849. Progress=0.549138

I would be interested to see the wallet file name on each of these log lines.

Would there be any interest in merging such a PR?
"      \"scriptPubKey\": \"<script>\" | { \"address\":\"<address>\" }, (string / json, required) Type of scriptPubKey (string for script, json for address)\n"
            "      \"timestamp\": timestamp | \"now\"                        , (integer / string, required) Creation time of the key in seconds since epoch (Jan 1 1970 GMT),\n"
            "                                                              or the string \"now\" to substitute the current synced blockchain time. The timestamp of the oldest\n"
            "                                                              key will determine how far back blockchain rescans need to begin for missing wallet transactions.\n"
            "                                                              \"now\" can be specified to bypass scanning, for keys which are known to never have been used, and\n"
            "                                                              0 can be specified to scan the entire blockchain. Blocks up to 2 hours before the earliest key\n"
            "                                                              creation time of all keys being imported by the importmulti call will be scanned.\n"
            "      \"redeemscript\": \"<script>\"                            , (string, optional) Allowed only if the scriptPubKey is a P2SH address or a P2SH scriptPubKey\n"
            "      \"pubkeys\": [\"<pubKey>\", ... ]                         , (array, optional) Array of strings giving pubkeys that must occur in the output or redeemscript\n"
            "      \"keys\": [\"<key>\", ... ]                               , (array, optional) Array of strings giving private keys whose corresponding public keys must occur in the output or redeemscript\n"
            "      \"internal\": <true>                                    , (boolean, optional, default: false) Stating whether matching outputs should be treated as not incoming payments\n"
            "      \"watchonly\": <true>                                   , (boolean, optional, default: false) Stating whether matching outputs should be considered watched even when they're not spendable, only allowed if keys are empty\n"
            "      \"label\": <label>                                      , (string, optional, default: '') Label to assign to the address (aka account name, for now), only allowed with internal=false\n"
            "    }\n"
            "  ,...\n"
            "  ]\n"
            "2. options                 (json, optional)\n"
            "  {\n"
            "     \"rescan\": <false>,         (boolean, optional, default: true) Stating if should rescan the blockchain after all imports\n"
            "  }\n"
            "\nNote: This call can take minutes to complete if rescan is true, during that time, other rpc calls\n"
            "may report that the imported keys, addresses or scripts exists but related transactions are still missing.\n"
            "\nExamples:\n" +
            HelpExampleCli("importmulti", "'[{ \"scriptPubKey\": { \"address\": \"<my address>\" }, \"timestamp\":1455191478 }, "
                                          "{ \"scriptPubKey\": { \"address\": \"<my 2nd address>\" }, \"label\": \"example 2\", \"timestamp\": 1455191480 }]'") +
            HelpExampleCli("importmulti", "'[{ \"scriptPubKey\": { \"address\": \"<my address>\" }, \"timestamp\":1455191478 }]' '{ \"rescan\": false}'") +
            "\nResponse is an array with the same size as the input that has the execution result :\n"
            "  [{ \"success\": true } , { \"success\": false, \"error\": { \"code\": -1, \"message\": \"Internal Server Error\"} }, ... ]\n");
    
    RPCTypeCheck(mainRequest.params, {UniValue::VARR, UniValue::VOBJ});