I don't think that will that change your Public IP address as allocated to you by your ISP?
I think you may be getting the internal IP address of your router confused with your public IP address, which is assigned to you and controlled by your ISP.
Your routers internal ip address is usually set as 192.168.001, rebooting the router doesn't normally change its Internal IP address either.
I’m not getting confused.
The external IP on most connections is set by DCHP.
Rebooting the router, and as Scutty suggests, waiting an hour, probably gets you a new number.
Why change the internal IP?
Last time I looked, ISPs charge extra for fixed IP addresses.
Unless things have changed, the IP will be dynamic unless it’s a premium service.