The name issue is a known bug. It's due to the parameter only allowing you to map Name, but if you're not using single field display it won't map correctly (only maps last name).
To change the VAT number label you can translate the CBSubs language string within CBSubs English language files to whatever you like. See the below for language usage information.
www.joomlapolis.com/cb-solutions/languages
You can find the CBSubs English language files below if it's installed.
components/com_comprofiler/plugin/language/cbpaidsubscriptions-en-gb/admin_language.php
As for removing some fields. The best way is to probably just use CSS. The below will hide them.
Code:
#cbfr_address_country_code,
#cbfr_address_state {
display: none !important;
}
The alternative is to modify the XML file used to generate that display, but your changes will be lost each time you upgrade.
components/com_comprofiler/plugin/user/plug_cbpaidsubscriptions/xml/edit.front.invoice.xml