I’ve been using Hyper-V for quite a while and have always just accessed a running VM from the Hyper-V Manager, but you can also use the Virtual Machine Connection. Or you can, in theory, but when you click the drop-down for Virtual Machine you see an error instead of a list of the available virtual machines:
I am a local admin on the host machine so, in theory, I should have permissions to everything. However, for some odd reason, you need to add extra permissions to be able to see this list of virtual machines. To do this open Local Users and Groups and find the Hyper-V Administrators group:
Add your user to this group and next time you open the Virtual Machine Connection you will see a list of available virtual machines to which you can connect.