I have my AWS lambda, lets call it Lambda-X.
There are other lambdas, I don\'t know their names, that consumes my Lambda-X via API call.
How do I determine t
Take a look at using AWS X-Ray to generate traces for your lambda invocations. You'll get a bit more information than CloudWatch logs will provide, and you can trace things across services to better understand where latency might be coming from. Here's a blog post with an example: https://docs.aws.amazon.com/xray/latest/devguide/xray-services-lambda.html
CloudWatch Metrics shows the number of invocations of each Lambda function. That will help you to determine which Lambda is being triggered the most frequently.
If that's insufficient, then each Lambda function obviously has a unique name. You could modify your initial Lambda functions to send that name as an additional 'source' event parameter to the invoked Lambda-X and then surface that as a custom metric.
Or you could scrape CloudWatch Logs, assuming that your lambdas emit an identifying log each time they invoke Lambda-X. Not a pretty solution, but might work for you.