Perform the following to set a Name tag to your NAT Gateway:
1. Sign in to the Amazon VPC console at https://console.aws.amazon.com/vpc/
2. Choose NAT Gateways
3. Move your mouse to the name field, click the edit logo.
4. Choose informational and meaningful name.

Via CLI:
aws ec2 create-tags –resources <NAT gateway ID> –tags Name = <Meaningful name>

References : https://docs.aws.amazon.com/vpc/latest/userguide/vpc-nat-gateway.html
CLI: https://awscli.amazonaws.com/v2/documentation/api/latest/reference/ec2/create-tags.html