I too had Skype just "appear" this morning when turning on the machine, and couldn't getting any success in removing it via the usual methods - Programs and Features, Remove from Startup within Task Manager, Find a Windows Service relating to it to stop, etc.
What I have found that has worked so far is:
- Going into Windows 10 Settings (Start -> Settings 'icon')
- Select 'Apps'
- Scroll through the list of apps until you find the 'Skype' entry. For me, I saw the install date (on the right hand side) as yesterday's date, so it was clearly a recent addition (and not one I authorised, or knew anything about I might add!)
- Click on the Skype app, 'Advanced Options' appear just under the 'Skype' name
- An 'Advanced Options' will appear just under the 'Skype' name, click on it
- Click on the 'Terminate' button
- Click on the 'Uninstall' button
As I said, this worked for me this morning, but I have seen reports of people stating the 'Uninstall' button within the 'Advanced Options' (Step 7 above) is greyed out for them, but still worth a try!