Having a look at the AWS documentation,
https://docs.aws.amazon.com/cognito/latest/developerguide/cognito-user-identity-pools-working-with-aws-lambda-triggers.html#cogni
Well, the simple solution would be like so, adding this to the "Pre Sign-up Lambda function", taking cue from your code:
// Modify an existing username...
event['request']['userAttributes']['name'] = "My_NAME";
// Add an additional attribute...
event['request']['userAttributes']['custom:sillyname'] = "ANY_NAME";
callback(null, event);
Considering you have added the custom:sillyname
attribute for the user pool.