I've never seen this happen before but if I type IP into Google it shows my IP, which a quick search shows the ISP as my VPN. That shouldn't happen, right?
Unless I misunderstand you, that's exactly what should happen. Try https://ipinfo.io/ and https://bgp.he.net/ You can dive deep on the Hurricane Electric site.
What used to happen was my IP showed as some third party ISP, not PureVPN. That third party was obviously connected to my VPN but the IP didn't actually show their name. I hope that makes sense.