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?
const UniValue& requests = mainRequest.params[0];
    
    bool fRescan = true;
    if (!mainRequest.params[1].isNull()) {
        const UniValue& options = mainRequest.params[1];
        if (options.exists("rescan")) {
            fRescan = options["rescan"].get_bool();
        }
    }
    WalletRescanReserver reserver(pwallet);
    if (fRescan && !reserver.reserve()) {
        throw JSONRPCError(RPC_WALLET_ERROR, "Wallet is currently rescanning. Abort existing rescan or wait.");
    }
    int64_t now = 0;
    bool fRunScan = false;
    int64_t nLowestTimestamp = 0;
    UniValue response(UniValue::VARR);
    {
        LOCK2(cs_main, pwallet->cs_wallet);
        EnsureWalletIsUnlocked(pwallet);
        
        now = chainActive.Tip() ? chainActive.Tip()->GetMedianTimePast() : 0;
        for (const UniValue& data : requests.getValues()) {
            GetImportTimestamp(data, now);
        }
        const int64_t minimumTimestamp = 1;
        if (fRescan && chainActive.Tip()) {
            nLowestTimestamp = chainActive.Tip()->GetBlockTime();
        } else {
            fRescan = false;