Is it possible to fetch container ID or Name of ecs fargate?

You can retrieve this information by querying the ECS Task Metadata Endpoint, exposed to your container via the ECS_CONTAINER_METADATA_URI environment variable. Here is an example response, taken from the documentation linked above:

{
    "DockerId": "43481a6ce4842eec8fe72fc28500c6b52edcc0917f105b83379f88cac1ff3946",
    "Name": "nginx-curl",
    "DockerName": "ecs-nginx-5-nginx-curl-ccccb9f49db0dfe0d901",
    "Image": "nrdlngr/nginx-curl",
    "ImageID": "sha256:2e00ae64383cfc865ba0a2ba37f61b50a120d2d9378559dcd458dc0de47bc165",
    "Labels": {
        "com.amazonaws.ecs.cluster": "default",
        "com.amazonaws.ecs.container-name": "nginx-curl",
        "com.amazonaws.ecs.task-arn": "arn:aws:ecs:us-east-2:012345678910:task/9781c248-0edd-4cdb-9a93-f63cb662a5d3",
        "com.amazonaws.ecs.task-definition-family": "nginx",
        "com.amazonaws.ecs.task-definition-version": "5"
    },
    "DesiredStatus": "RUNNING",
    "KnownStatus": "RUNNING",
    "Limits": {
        "CPU": 512,
        "Memory": 512
    },
    "CreatedAt": "2018-02-01T20:55:10.554941919Z",
    "StartedAt": "2018-02-01T20:55:11.064236631Z",
    "Type": "NORMAL",
    "Networks": [
        {
            "NetworkMode": "awsvpc",
            "IPv4Addresses": [
                "10.0.2.106"
            ]
        }
    ]
}