lambda@edge functions defaulting to aws/lambda/undefined log group

I'm creating lambda@edge functions via the CDK, and each of these functions is defaulting to a log group of /aws/lambda/undefined.

From the documentation it seems like the log group should be automatically created with the {functionName}, but I do not want to set that explicitly and allow CDK to figure that out.

Here's the code I'm using to create my edge functions:

export enum EdgeFunctionName {
  HTTP_HEADERS = 'http-headers',
  SSO_AUTH = 'sso-auth',
  SSO_CALLBACK = 'sso-callback',
  GATEWAY = 'gateway',
}

const EDGE_FUNCTIONS: EdgeFunctionConfig[] = [
  { name: EdgeFunctionName.HTTP_HEADERS, eventType: LambdaEdgeEventType.VIEWER_REQUEST },
  { name: EdgeFunctionName.SSO_AUTH, eventType: LambdaEdgeEventType.VIEWER_REQUEST },
  { name: EdgeFunctionName.SSO_CALLBACK, eventType: LambdaEdgeEventType.VIEWER_REQUEST },
  { name: EdgeFunctionName.GATEWAY, eventType: LambdaEdgeEventType.ORIGIN_REQUEST, includeBody: true },
];

export const createEdgeFunctions = (
  scope: Construct,
  stage: Stage,
  region: Region,
  env: DeploymentEnvironment,
): Map<EdgeFunctionName, EdgeLambda> => {
  const lambdaRole = createLambdaEdgeRole(scope, env, region, stage);
  return new Map(
    EDGE_FUNCTIONS.map((edgeFunction: EdgeFunctionConfig) => [
      edgeFunction.name as EdgeFunctionName,
      {
        functionVersion: new experimental.EdgeFunction(
          scope,
          `EdgeFunction${edgeFunction.name}-${stage}-$region}`,
          getEdgeFunctionOptions(edgeFunction.name, lambdaRole),
        ).currentVersion,
        eventType: edgeFunction.eventType,
        includeBody: edgeFunction.includeBody,
      },
    ]),
  );
};

export const getEdgeFunctionOptions = (functionName: string, lambdaEdgeRole: Role): experimental.EdgeFunctionProps => {
  return {
    runtime: Runtime.NODEJS_18_X,
    handler: 'index.handler',
    code: Code.fromAsset(`dist/lambda-edge/${functionName}/index.zip`),
    role: lambdaEdgeRole,
    timeout: Duration.seconds(5),
  };
};

Only when I pass in functionName in the edge function options does the log group name get generated correctly, but it's my understanding that CDK should generate a name for the edge function based on the ID set in the EdgeFunction constructor and the log group should be created with that same name.