How can I change name of my siri's name?

If you wish to see a feature enhancement, you can make a request to Apple using their feedback page here, https://www.apple.com/feedback/iphone.html

This is a user to user support forum, and Apple does not participate here. Good luck.

I wonder if this can be requested for development.

I have several devices that respond to 'Hey, Siri' when I want to ask a question. If my iMac, MacBook, iPad and iPhone are in the same room, they all want to help.

Alexsa allows for some configuration, and Siri should be able to do this as well.

Not possible.