How to set Lambda function name?

Function name can be assigned at the time of creation, for example if you are creating a Lambda function using cloud formation, the you can use FunctionName: <name>. If you don't specify a name, AWS CloudFormation generates one. So after an auto generated name has been assigned, then the closest thing you can do is assign Alias. Please follow the documentation shared below to create an alias. https://docs.aws.amazon.com/lambda/latest/dg/configuration-aliases.html

A bit cryptic here: https://github.com/aws/aws-extensions-for-dotnet-cli/blob/master/src/Amazon.Lambda.Tools/LambdaDefinedCommandOptions.cs as it refers it as AWS Lambda function name

The documentation here says to enter the function name when deploying the Lambda function, but this procedure does not set the function name?
I apologize if I am mistaken, but is deploying done differently than the procedure in the following document?
https://docs.aws.amazon.com/toolkit-for-visual-studio/latest/user-guide/lambda-creating-project-in-visual-studio.html#publish-to-lam

What is incorrect in my file? VS2022 publish Lambda to AWS successfully, The question how to set name,

Your file looks correct, check if the Function Name is populating on the publish screen while you are Uploading Lambda to AWS. If you do not see the name in Function Name field then try to re create your json file using the following reference. https://github.com/iammukeshm/aws-lambda-dotnet-6/blob/master/HelloLambda/aws-lambda-tools-defaults.json