You can change the MySQL port in the /etc/my.cnf file:
Then restart MySQL:
I did this change on my machine as a test and had no issue whatsoever changing it. Here's the results showing it began listening on that port after the change:
Notice the --port=6446 part in the ps aux return?
[root@itchy:~] # ps aux|grep mysql
root 10660 0.3 0.1 6744 1076 pts/0 S 07:29 0:00 /bin/sh /usr/bin/mysqld_safe
mysql 10805 3.8 15.5 1510596 155372 pts/0 Sl 07:29 0:00 /usr/sbin/mysqld
--basedir=/ --datadir=/var/lib/mysql --user=mysql --pid-file=/var/lib/mysql/hostname.com.pid
[root@itchy:~] # lsof -i :6446
COMMAND PID USER FD TYPE DEVICE SIZE NODE NAME
mysqld 10805 mysql 12u IPv4 60642652 TCP *:6446 (LISTEN)
As a final note, I did also check PhpMyAdmin and cPanel > MySQL Databases area. Both were working for me after this change, so this did not impact the various cPanel areas working on my server.
[root@itchy:~] # netstat -an|grep :6446
tcp 0 0 0.0.0.0:6446 0.0.0.0:* LISTEN