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?
{
    return BerkeleyBatch::VerifyEnvironment(wallet_path, errorStr);
}
bool WalletBatch::VerifyDatabaseFile(const fs::path& wallet_path, std::string& warningStr, std::string& errorStr)
{
    return BerkeleyBatch::VerifyDatabaseFile(wallet_path, warningStr, errorStr, WalletBatch::Recover);
}
bool WalletBatch::WriteDestData(const std::string &address, const std::string &key, const std::string &value)
{
    return WriteIC(std::make_pair(std::string("destdata"), std::make_pair(address, key)), value);
}
bool WalletBatch::EraseDestData(const std::string &address, const std::string &key)
{
    return EraseIC(std::make_pair(std::string("destdata"), std::make_pair(address, key)));
}
bool WalletBatch::WriteHDChain(const CHDChain& chain)