EventBridge name

I have a new problem now. I change event from schedule to pattern. However I notice the rule name becomes auto-generated, which is not expected because I need a specific name e.g. stage-user-my-function. I tested to add name to eventBridge section, but it doesn’t work. I appreciate any suggestions!

The old configuration with schedule:

my-function:
    handler: my_function.lambda_handler
    memorySize: 256
    timeout: 30
    events:
      - schedule:
          name: stage-user-my-function
          description: "Triggers my function"
          rate: rate(1 minute)
          enabled: false

The new configuration with pattern match:

my-function:
    handler: my_function.lambda_handler
    memorySize: 256
    timeout: 30
    events:
        - eventBridge:
            name: stage-user-my-function # <-------- I want to force to use a specific name, but adding here with name doesn't work
            eventBus: arn:aws:events:<region>:<account-id>:event-bus/default
            pattern:
            account:
                - ${self:custom.accountId}