How is this possible? - Showing now Console Log and Terminal

Go into Terminal and type each of these commands:

sudo scutil --get ComputerName
sudo scutil --get LocalHostName
sudo scutil --get HostName

Compare what you get to what you are seeing in the Terminal prompt, and in the Console.

My concern is that Supah-Pablo-6 is a recent entry in both the Console Log and the Terminal, but that user name is someone who uses my internet connection and is not me.

To my knowledge, this person has never used my computer, and we are not particularly close. That's the name of a device that belongs to the user who is now connected to my home network.

He has the authority to use the shared connection, therefore I can't remove it. However, I'm not sure if this means that he has access to my computer in for this to occur.

I can't tell what you mean by "that user name", "this person", "that's the name of a device" ... "He has the authority to use the shared connection" ... there are multiple names shown in your screenshots and I can't tell which you are referring to in these quoted segments. And what shared connection are you talking about here? Is the person connected to your router? Or something else?

What do you mean by "we are not particularly close"? How does that relate to your concern. What is your concern? Is it that someone else is controlling your computer remotely? If so, what leads you to have that concern?

What happens if you change the Computer Name under Sharing in System Preferences as well as the NETBIOS Name? I would restart your computer afterwards. It will flush the arp cache.

I would also turn off all Sharing services at the same time.

If you haven't restarted your Mac since your phone was stolen it may still be showing up in the arp cache.

I would start by implementing the following if you haven't done so already:

• Under System Preferences --> Security & Privacy --> General
  • Change Password
  • Require Password after 15 minutes or what you feel comfortable with.
• Under System Preferences --> Security & Privacy --> File Vault
  • Turn on file vault
• Under System Preferences --> Security & Privacy --> Firewall
  • Turn on the firewall
  • Under Firewall Options - tick everything unless you need access. Remove the applications under Block all incoming connections unless you need them. Alternatively you can block them.
• Under System Preferences --> Security & Privacy --> Privacy
  • Review access for each service, especially Full Disk Access
• Change you Apple ID password
• Under System Preferences --> Software Update
  • Apply the latest updates
• Under System Preferences --> Users & Groups
  • Ensure the Guest User is off
  • Ensure at least one user account is admin
  • Change password of both accounts if you haven't done so already.
  • Review Login Items - is anything out of place?
  • Login Options
    • Turn off Automatic Login
• Consider installing and using (malware is possible on macOS):
  • Little Snitch
  • ClamXAV
• Speak to your flatmates and change your router's WiFi password to something long and complicated. There are tools which will quickly guess WiFi passwords if they are short and simple.
• Monitor the output of arp -a to see if devices return or not.

Good luck.

I am confused by some of the information you provided.

Was your stolen phone using your Apple ID with Find My iPhone enabled? If so, you can erase it completely remotely.

I don't understand your situation with the router. Is this your router? Are you connecting to someone else's router? Do you have an ethernet hard line? If so, suggest you obtain your own router and connect it to that hard line and lock down all access to your router (except for you). Even better, connect your Mac to the hard line instead of WiFi.

Other things you can do:

• Change your user password for your Mac.
• Change your Apple ID password.
• Go to Apple ID in System Preferences and make sure all old devices are removed from your list of devices, including the stolen one(s).
• Go to System Preferences Sharing. Turn off all access (uncheck all boxes).
• Go to System Preferences, Security and Privacy, Firewall, make sure Firewall is "on," select Firewall Options ... Consider blocking all incoming connections. Consider turning on Stealth Mode. Look at other options and think about turning them on (or off) to enhance security.
• Consider using FileVault. Consider a firmware password.

If you are having things stolen and/or physical access to your stuff is not secure, having good passwords and things like FileVault and firmware password might be important. With those enabled, someone accessing your computer is completely locked out, they can't do anything. I can't tell but it sounds to me like you need to move to a new place!

If you have another phone now, make sure you have a long passcode. Maybe purchase a safe to lock your stuff up when you aren't there?

If you change all those passwords, disable all remote access, and then restart your computer, all remote connections are broken and won't be resumable as long as no one else knows your passwords.