How to rename an AWS API Gateway API instance?

Yes it's available in the API or CLI.

In the API you use a PATCH request on the 'name' field. http://docs.aws.amazon.com/apigateway/api-reference/resource/rest-api/

In the CLI, see docs http://docs.aws.amazon.com/cli/latest/reference/apigateway/update-rest-api.html

The PATCH op is 'replace' and the path would be '/name'

Edit: Thanks @Canotto90 for the example

aws apigateway update-rest-api --rest-api-id IDOfTheAPIThatNeedsTobeUpdated --patch-operations op=replace,path=/name,value=NewName

From https://console.aws.amazon.com/apigateway -> Select API by Name -> Settings -> General Settings -> Name

It turns out, there is now a way to rename the API!

Under the Amazon API Gateway service, select APIs. You will see the list of your APIs.

Now, click the little cog wheel in the top right corner of the API that you wish to rename...

Simply change the name, hit save, and you're good!

Here is how you can get the list of APIs and their IDs:

aws apigateway get-rest-apis

Use the Id to update name of API as mentioned by Canotto90 above:

aws apigateway update-rest-api --rest-api-id IDOfTheAPIThatNeedsTobeUpdated --patch-operations op=replace,path=/name,value=NewName