Yes. You can change the private IP address of your router, but not the public IP address. Read on to understand the difference between the both and why you are able to change the private IP address but not the public IP address.
Understanding private and public IP address on router
Private IP address is the IP address which is assigned to your local network. For example, you would have observed the IP address 192.168.1.1 or 192.168.0.1 which your router comes pre-configured with.
This IP address is reserved for local usage only. These IP address cannot be used on the internet.
The IANA, which stands for internet assigned numbers authority has allocated a certain block of IP address for private use. The list is provided below.
10.0.0.0 to 10.255.255.255
172.16.0.0 to 172.31.255.255
192.168.0.0 to 192.168.255.255
Public IP address is the IP address which is allocated by your Internet service provided (ISP). These are allocated from outside the block provided above and cannot be used for your internet network.
Pubic IP address is assigned to the router for connecting to the internet.
Can I change private IP address of my router
Yes. You can change the private IP address on your router. You can change it to any IP address which is provided in the above block. This allowed by the IANA. As an example, your friends router at a different location can have the same IP address as yours.
This is because both are configured only for the internal network and does not reach the internet.
Can I change public IP address of my router
No. You cannot change the public IP address of your router. This is allocated by the ISP. The ISP allocates public IP address for each router connected to the internet and this is unique for each router.
You do not have the authority to change it.
It can be understood that you can change the private IP addres of your router but not the public IP address , since you have control only over the private IP address. The public IP address is controlled by the ISP.
Product Recommendation
Firewall router for home – ASUS WiFi 6 Router (RT-AX3000)
Mesh router for 5000 sqft home – NETGEAR Orbi Whole Home Tri-band Mesh WiFi 6 System (RBK852)