So if a provider has software that blocks you from using their internet to connect to, say, Spotify or Skype. Is there a way to block your computer from communicating that this program is running? Or to disguise it as another program?
This can't be done simply on your computer. You will need an SSH server which you will use to establish an encrypted tunnel:
Because your traffic is encrypted, the provider will not be able to view and thus not block your traffic. Note that the provider might still try to block you on DNS level. To bypass such a protection you should use public DNS servers, preferably these DNS requests also should be sent through your SSH tunnel.