In theory, if I connected to my VPN, and then connected to my employer's VPN, then they would see my VPN provider's server as what they would be connected to. In other words, they would think that my VPN provider's server was my computer, and they would see only the traffic intended to go to them. That was my theory, anyway.
I work from home, so I'm not connected to their WiFi. I'm connected to my WiFi, and load their VPN software when I need to do work related things.
Lot of effort to go through to do personal stuff at work, uhm, when you should be working.
Point well taken. However, I'm on call 24/7, and it just would make it easier if I didn't have to say "I'm doing work stuff, so connect to that VPN. Now I'm doing personal stuff, so connect to my personal VPN provider." Also, sometimes I have to be online and connected to work, but really only to listen in and jump in if an issue arises that I'm responsible for.
Gotcha
In that case, two devices would be the most secure way to keep the two concerns separate. Depending on the devices, it could take up extra desk or table space.
I would think the second VPN connected to would be the one to see what you final destination url is but they might not know it’s you. That could seem suspicious to them.
I did not know that VPN business accounts track employees of that business. Kind of an alternate use of a VPN. We have to assume the VPN knows the MAC address(device specific) of your devices too IF there’s only one VPN. If two, the second one would get the MAC address of the first VPN. Then the question would be, will that raise suspicion?
Two devices, one work, one personal would be best imho.