Any brand of router, or any computer on a local network for that matter, can be set to use 192.168.0.1 or a comparable private IPv4 address.
The popularity of 192.168.0.1 is also attributable to the manufacturers. IP address 192.168.0.1 is considered private as it falls within the range 192.168.0.0 up to 192.168.255.255 which are IP addresses issued to computers and devices on a single network. All these IPs can’t be accessed from the Internet (Network Address Translation (NAT) is required for Internet communication). The private IPs can be used in a network, and it is good to know that only one device can have this IP 192.168.0.1.
The address 192.168.0.1 is also referred to as a gateway address, with the gateway meaning network access point (the router).