I wonder if we can change the default port TCP port number(179) used during the BGP session. I recently came across a document BGP Vulnerability Testing: Separating Fact from FUD. It suggested considering source port randomization in BGP for security purposes.
Asking such a question, you should summarize the essence of the linked paper - few potential responders are likely to click the link and skim the paper.
The paper seems to be about mitigating a brute-force attack on BGP peers, spoofing the source IP address and source port of likely peers and trying to inject malicious information or forcing a TCP connection reset, essentially a DoS attack.
With a fixed source port for a running BGP-over-TCP session, the attacker needs to guess the current sequence number (with a chance of 1:232. Randomizing the source port would increase the difficulty by the port number size (16 bits) to 1:248.
While that seems doable and does seem to solve the problem mathematically, I'd suggest a more practical approach - without any necessity to change a BGP entity, which is often embedded in a border gateway and not easy to change. Also, sequence numbering might not be truly random, so an attacker could start with a much lower complexity, and then adding 16 bits wouldn't really help.
BGP takes place at a public or private IX. If the IX simply filters the peering segment(s) for inbound destination port 179, security improves much more than port randomization does. Also, proper monitoring a BGP entity is pretty much mandatory, and a brute-force, high-rate attack shouldn't go unnoticed for an extended time anyway.
'We' can only change the default port number for any given service if the organization who makes the service software allows a configuration to do so. So if your router has the option to configure the BGP service to listen on a different port and use a different source port, then you can do so.
If you can, it would not accomplish much. Anyone who wanted to find a BGP service to abuse could just do a port scan until they find it. If you want to actually secure your BGP service, use an access list to limit source IP addresses that can connect using the standard BGP port and authentication for the peer relationship.