User profile disks are named by the users SID (Security Identifier) and in order to know match a disk to a user there is a tool called Sidder which will help you do just that and can be downloaded from:
To extend the UPD, you will need to run the following commands in an elevated Powershell:
Enable-WindowsOptionalFeature -Online -FeatureName Microsoft-Hyper-V -All -NoRestart
This will enable Hyper-V in Online mode on the FBU server. The server will need a restart in order to fully configure the feature but the -NoRestart flag should prevent that from happening so you can schedule it at your convenience. Once you have the feature installed run the following command to install the required powershell cmdlets:
Once you have that installed you can run the following command to resize your UPD
Resize-VHD -Path 'C:\profile\profiledisk.vhdx' -SizeBytes XXGB
After running this mount the .vhdx file and open disk manager and there will be unallocated space for the UPD, extend the disk, then unmount it.
Please note that you can extend and shrink your UPD using this method so be careful if you intend to use it for shrinking the size of a UPD as you may cause it to become corrupt or lose data.