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?
}
        for (const UniValue& data : requests.getValues()) {
            const int64_t timestamp = std::max(GetImportTimestamp(data, now), minimumTimestamp);
            const UniValue result = ProcessImport(pwallet, data, timestamp);
            response.push_back(result);
            if (!fRescan) {
                continue;
            }
            
            if (result["success"].get_bool()) {
                fRunScan = true;
            }
            
            if (timestamp < nLowestTimestamp) {
                nLowestTimestamp = timestamp;
            }
        }
    }
    if (fRescan && fRunScan && requests.size()) {
        int64_t scannedTime = pwallet->RescanFromTime(nLowestTimestamp, reserver, true );
        pwallet->ReacceptWalletTransactions();
        if (pwallet->IsAbortingRescan()) {
            throw JSONRPCError(RPC_MISC_ERROR, "Rescan aborted by user.");
        }
        if (scannedTime > nLowestTimestamp) {
            std::vector<UniValue> results = response.getValues();
            response.clear();
            response.setArray();
            size_t i = 0;
            for (const UniValue& request : requests.getValues()) {