public async Task InsertInBulk(IList<string> userNames)
{
    var sqls = GetSqlsInBatches(userNames);
    using (var connection = new SqlConnection(ConnectionString))
    {
        foreach (var sql in sqls)
        {
            await connection.ExecuteAsync(sql);
        }
    }
}

private IList<string> GetSqlsInBatches(IList<string> userNames)
{
    var insertSql = "INSERT INTO [Users] (Name, LastUpdatedAt) VALUES ";
    var valuesSql = "('{0}', getdate())";
    var batchSize = 1000;

    var sqlsToExecute = new List<string>();
    var numberOfBatches = (int)Math.Ceiling((double)userNames.Count / batchSize);

    for (int i = 0; i < numberOfBatches; i++)
    {
        var userToInsert = userNames.Skip(i * batchSize).Take(batchSize);
        var valuesToInsert = userToInsert.Select(u => string.Format(valuesSql, u));
        sqlsToExecute.Add(insertSql + string.Join(',', valuesToInsert));
    }

    return sqlsToExecute;
}