Can a website identify a device when IP address is changed

[bigbigI]

Can a website identify a particular device when the IP adress is changed, such connecting throught mobile data or connecting to another router?

[Voodoo]

Yes. The Browser's HTTP header contains the string "User-Agent: ........" and this string says a lot of things about you:
- Operating System,
- Browser (chrome/firefox,...),
- etc.

[Chrispcritters]

Cookies also...