Install AWS CLI:
curl "https://s3.amazonaws.com/aws-cli/awscli-bundle.zip" -o "awscli-bundle.zip"
sudo apt-get install unzip
unzip awscli-bundle.zip
sudo ./awscli-bundle/install -i /usr/local/aws -b /usr/local/bin/aws
Get the tags for the current instance:
aws ec2 describe-tags --filters "Name=resource-id,Values=`ec2metadata --instance-id`"
Outputs:
{
    "Tags": [
        {
            "ResourceType": "instance", 
            "ResourceId": "id", 
            "Value": "Webserver", 
            "Key": "Name"
        }
    ]
}
Use a bit of perl to extract the tags:
aws ec2 describe-tags --filters \
"Name=resource-id,Values=`ec2metadata --instance-id`" | \
perl -ne 'print "$1\n" if /\"Value\": \"(.*?)\"/'
Returns:
Webserver