Use CreateLogStream with an Amazon SDK or command line tool

    using System;
    using System.Threading.Tasks;
    using Amazon.CloudWatchLogs;
    using Amazon.CloudWatchLogs.Model;

    /// <summary>
    /// Shows how to create an Amazon CloudWatch Logs stream for a CloudWatch
    /// log group.
    /// </summary>
    public class CreateLogStream
    {
        public static async Task Main()
        {
            // This client object will be associated with the same AWS Region
            // as the default user on this system. If you need to use a
            // different AWS Region, pass it as a parameter to the client
            // constructor.
            var client = new AmazonCloudWatchLogsClient();
            string logGroupName = "cloudwatchlogs-example-loggroup";
            string logStreamName = "cloudwatchlogs-example-logstream";

            var request = new CreateLogStreamRequest
            {
                LogGroupName = logGroupName,
                LogStreamName = logStreamName,
            };

            var response = await client.CreateLogStreamAsync(request);

            if (response.HttpStatusCode == System.Net.HttpStatusCode.OK)
            {
                Console.WriteLine($"{logStreamName} successfully created for {logGroupName}.");
            }
            else
            {
                Console.WriteLine("Could not create stream.");
            }
        }
    }

The following command creates a log stream named 20150601 in the log group my-logs:

aws logs create-log-stream --log-group-name my-logs --log-stream-name 20150601