Criteria for Common Name of Certificate Authority and how it affects SSL certificates

Criteria for Common Name of Certificate Authority and how it affects SSL certificates

It is not clear to me how the Common Name affects a certificate authority and the certificates that are ultimately created. For example, I have this simple script that creates some files for a certificate authority auto-generated/ca.* and an ssl certificate for hello.test.com.

#!/bin/bash

ORG="ABTEST"
CN="blahblahthisdoesnotmatterquestionmark"
certdir="./auto-generated"

mkdir -p $certdir;
cp entity.cnf $certdir"/";

## Create certificate authority
openssl genrsa -out $certdir/ca.key 2048
openssl req -x509 -sha256 -nodes -key $certdir"/ca.key" -subj "/C=CA/ST=ON/O="$ORG"/CN="$CN -days 3650 -out $certdir"/ca.crt"

## Create entity certificate

# Private Key
openssl genrsa -out $certdir/entity.key 2048
# CSR
openssl req -new -sha256 -nodes -key $certdir"/entity.key" -config $certdir"/entity.cnf" -out $certdir"/entity.csr"
# Certificate
openssl x509 -req -in $certdir"/entity.csr" -CA $certdir"/ca.crt" -CAkey $certdir"/ca.key" -CAcreateserial -out $certdir"/entity.crt" -days 500 -sha256 -extensions v3_req -extfile $certdir"/entity.cnf"

entity.cnf

[req]
distinguished_name = req_distinguished_name
x509_extensions = v3_req
prompt = no
[req_distinguished_name]
C = CA
ST = ON
L = Windsor
O = Ankle
OU = Hello
CN = hello.test.com
[v3_req]
keyUsage = critical, digitalSignature, keyAgreement
extendedKeyUsage = serverAuth
subjectAltName = @alt_names
[alt_names]
DNS.1 = hello.test.com

It seems I can change the variable CN=blahblah... to anything I want and it doesn't have any technical/functional effects on the entity.crt. Meaning I can go to Firefox browser and visit https://test.hello.com and see a green lock icon if I follow these steps:

1. choose any value I want for CN=blahblah...
2. create the ca.* and entity.* files
3. set up Apache Web server on the computer hello.test.com
4. tell Apache web server to use entity.* and ca.crt for ServerName hello.test.com
5. systemctl restart apache2
6. import ca.crt into my FireFox web browser

So my question is, what are the criteria for choosing a Common Name for a certificate authority? What do I need to be aware of to make sure client applications can verify my certificates?