By definition, you address your QC server by
http:// name_or_IP_of_QCserver : port / qcbin
This is due to the QC/ALM ''application'' being served by JBOSS or JETTY (11.5x and later). You can supress the port if you use port 80 - it will be assumed and you don't need to specify the port. If using 8080 (default) or other port than 80, you must specify in the URL.
If you want to have a DIFFERENT address and have it ''resolve'' it to the original one behind the scenes, you need to do that on the domain lookup table internal to your company. Here, you can establish various ''aliases'' for
http:// name_or_IP_of_QCserver : port / qcbin (in your case http://qcmachine:8080/qcbin).
In your situation, it is likely that you can address this Server (generically) with either the name ''qcmachine'' or ''qcmachine.company.org'', so getting the address ''qcmachine:8080'' to resolve to ''qcmachine.company.org'' (without port) may be tricky.
If in your domain table, ''qcmachine'' or ''qcmachine.company.org'' behave exactly the same, you may need to use port 80 instead of 8080. Then users could address your QC server by IP address or ''qcmachine'' or ''qcmachine.company.org'' without using any port number.