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?
{
    bool fLabelFound = false;
    CKey key;
    pwallet->GetKey(keyid, key);
    for (const auto& dest : GetAllDestinationsForKey(key.GetPubKey())) {
        if (pwallet->mapAddressBook.count(dest)) {
            if (!strAddr.empty()) {
                strAddr += ",";
            }
            strAddr += EncodeDestination(dest);
            strLabel = EncodeDumpString(pwallet->mapAddressBook[dest].name);
            fLabelFound = true;
        }
    }
    if (!fLabelFound) {
        strAddr = EncodeDestination(GetDestinationForKey(key.GetPubKey(), pwallet->m_default_address_type));
    }
    return fLabelFound;
}
static const int64_t TIMESTAMP_MIN = 0;
static void RescanWallet(CWallet& wallet, const WalletRescanReserver& reserver, int64_t time_begin = TIMESTAMP_MIN, bool update = true)