If you are calling startExecution then there is a way that I mention bellow. But seems like your question is related to calling Step Functions from other service (Maybe EventBridge) that my answer is not covering it. For that if there is no direct way, you can call a Lambda function and from Lambda call Step Function startExecution.
StartExecution accept this:
{
"input": "string",
"name": "string",
"stateMachineArn": "string",
"traceHeader": "string"
}
And name
is what you are looking for:
The name of the execution. This name must be unique for your AWS
account, region, and state machine for 90 days. For more information,
see Limits Related to State Machine Executions in the AWS Step
Functions Developer Guide.
A name must not contain:
white space
brackets < > { } [ ]
wildcard characters ? *
special characters " # % \ ^ | ~ ` $ & , ; : /
control characters (U+0000-001F, U+007F-009F)
To enable logging with CloudWatch Logs, the name should only contain
0-9, A-Z, a-z, - and _.
Link: https://docs.aws.amazon.com/step-functions/latest/apireference/API_StartExecution.html
You have similar option when starting the Execution from AWS CLI, Console,...