Changed Fullname and Account name but not Home directory, now blank "Admin" page [duplicate]

My Father died last year and I inherited his Mac Mini. My wife has retired and we are trying to set up the mini for her use but the changes we want to make require admin access and we do not have the information my father used to set up the machine.

Is it possible to reset the admin information without having the old information? If so, how would I go about it?

I am not a Mac user usually so any guidance will have to be pretty simple!

With macOS Catalina and many recent macOS - the built in tools guide everyone how to reset admin permissions without needing any of the single user mode boot tricks of old (left at the bottom for posterity and people running OS that were shipped before 2015)

Now - follow the official Apple triage steps: https://support.apple.com/en-us/HT202860

Instead of single user mode, boot to recovery and use the Terminal Utility. Then you can remove the .AppleSetupDone file from:

/Volumes/Macintosh\ HD\ -\ Data/private/var/db 

There are many ways to reset the login password without installation media, here are three:

Change the password in single user mode

1. Hold ⌘+S on startup
2. mount -uw / (fsck -fy is not needed)
3. launchctl load /System/Library/LaunchDaemons/com.apple.opendirectoryd.plist (or /System/Library/LaunchDaemons/com.apple.DirectoryServices.plist in 10.6)
4. dscl . passwd /Users/username (without a trailing slash) and enter a new password. You can ignore the error about com.apple.DirectoryServices.plist.
5. reboot

Create a new admin account

1. Hold ⌘+S on startup
2. mount -uw / (fsck -fy is not needed)
3. rm /var/db/.AppleSetupDone
4. reboot
5. Go through the steps of creating a new account. You can leave all fields in the personal information step blank.
6. After logging in to the new account, go to the Users & Groups preference pane
7. Select the old account, press the Reset Password... button, and enter a new password

Restart and enter Recovery mode (for 10.7 Lion and newer OS only)

1. Hold ⌘+R on startup
2. Open Terminal from the Utilities menu
3. Type resetpassword and follow the instructions

Using iCloud Recovery Mode (10.9.x & newer)

1. After incorrectly entering a user password three times at the Mac login screen, a message appears saying "If you forgot your password, you can reset it using your Apple ID"
2. Click the arrow button to bring up a "Reset Password" dialog
3. Enter the Apple ID login information that is tied to the OS X user account and click “Reset Password”
4. Click “OK” to confirm the new keychain creation
5. Enter and verify a new password, fill out the password hint field, and again click on “Reset Password”
6. Click “Continue Log In” to login as the user account with the reset password

I'm sorry to hear about your father.

It is possible to reset the admin password to a Mac quite easily providing you have the correct install disc to match the version of the software that is running on the computer. Resetting the password does not delete any of the information on the Mac, but it will prevent you from gaining access to other passwords that are saved in the system for things like mail accounts or wifi keys that have previously been entered and saved by the original user. Once you have changed the password you will be prompted to create a new Keychain, which is the name of the place where these other passwords are saved.

Once you have admin access you can create or delete accounts. There is a support article on the Apple website with info on how to reset the password here: http://support.apple.com/kb/HT1274

If you don't have the install disc or need more help, I'd suggest booking an appointment at the Genius Bar at your local Apple Store and they will help you reset it at no charge.