My company has a SSL certificate for *.mycompany.com. We use this certificate for many critical services.
Marketing team owns www.mycompany.com website (WordPress) and wants a SSL certificate for it.
Can we issue a specific certificate for www.mycompany.com?
Yes. as far as the certificate is concerned there is no relationship between different servers. You could have five different servers with five different certificates and as long as each one of them is valid there wouldn’t be a problem. (it might cause a problem if the certificate changes mid-session)
You should however be aware that http://www.example.com would also be usable as a certificate for any of your other ‘critical’ services that operate on http://www.example.com, you could have a security issue there.