Without admin capes, you'll need to create a new Admin user. See here: Updated to High Sierra, all Admin accounts now Standard - Apple ...
This is the important part as posted by dr_manfred:
Start up the Mac whilst holding down ⌘-S. After a few moments, you'll see the Mac boot to the command line.
Before continuing, the filesystem must be checked and mounted, so files are't immediately accessible to interact with. To do this, enter the two commands that are displayed within the prompt, one at a time.
The following command will check the filesystem to ensure there are no problems. Enter:
/sbin/fsck -fy
The next command will then mount the filesystem for it to be accessible:
/sbin/mount -uw /
With the filesystem mounted and accessible, it's time to remove the file so OS X will re-run Setup Assistant:
rm /var/db/.AppleSetupDone
Reboot and the Setup Assistant will run. Create a new user when prompted and then use that user to give your other user Admin capability.
What is the background on the wrong user name?
If you got the Mac from someone else, you should completely erase it and start over. You will have to back up any data you created before erasing and reinstalling.
If you got the Mac from someone you know and trust, it would just be better to create your own user, but the Mac will still be licensed to the original owner. Completely erasing the Mac in Internet Recovery and reinstalling the OS is the only way to transfer the license.