How to identify user of my website in IP non-based way? I'm looking for something like fingerprint2.js, but user identity should be the same no matter if user change browser or ip address. One device = one const identifier.
Short answer is you can't, at least not reliably, especially with just JavaScript.
Existing fingerprinting techniques leverage what are essentially considered by vendors as security flaws in the information the browser exposes to try and come up with a unique "fingerprint" for a user. This relies on browser-specific features, though.
Something which provided enough info/allowed you to store data which escapes the sandbox of a specific browser and persistently identifies a user computer-wide would almost certainly be considered a serious security flaw, and would be patched rather quickly.
See this question for more details.