In serverless version above 1.27.3 one can set a custom stackName.

provider:
   stackName: my-custom-name

In main serverless they are using this getStackName from this code to fetch the stackname:
https://github.com/serverless/serverless/blob/cbc5e3c4e199a08650b02def8d1f9e91a13e7844/lib/plugins/aws/lib/naming.js

Used as in serverless, if you get the this reference correct you are done:

const stackname = this.provider.naming.getStackName();