I want to remove the VAT portion of the title when creating a new account.
You can see inside of
This part of code:
If you search for this block you arrive to this path:
Inside this file you can see this:
echo $this->__('Tax/VAT number')
You can change with some conditions on registration page.
It looks like you are using a custom theme. You should ask the provider where is the phtml you need to modify and/or turn on template path hints to see it by yourself.
To turn on Template hints go to System -> Configuration -> Developer and select on the top left the website or store you are using. After that you will see a select called Template Path Hints. Turn it on. Guide with images here. After that you will be able to remove/modify the TAX/VAT field in the correct phtml.