There are a few easy ways in which you can find your computer's name:

By Tags on the Computer

Apple Mac:

UNT labels each computer with a physical Asset Tag sticker, located usually on the backside of the computer, either on the top or bottom.
Use the UNT Asset Tag. The computer name should be "CAS-" appended with the UNT asset number, as such: CAS-12345.

Dell Laptops and Desktops:

Dell labels each system with a unique physical Service Tag (ST) sticker, located usually on the top of desktops and the bottom of laptops. It is a combination of letters and numbers.
Use the Service Tag. The computer name should be "CAS-" appended with the Dell Service Tag, as such: CAS-12ABC34

From the Login Screen

1. At the login screen, press Ctrl-Alt-Del.
2. Click OK, if you understand to the warning.
3. Type .\ in the username field.
4. you will see your computers name show up under the password field; CAS-WKTST-7X64 in this image:
   

System Properties

1. If you have Windows 7, right-click Computer and select Properties.
   1. Your computer name is listed as: Computer name
   2. Your full computer name is listed as: Full computer name

Run a quick command

1. Press: Windows + R to open the Run Window
Alternatively, Click: Start Menu then Click: Run

2. Paste the following in the text field:
cmd /k hostname

?

3. Press Enter or click OK

4. A Command Prompt window will open and your computers name is on the first line of the black background.

Hostname on macOS

1. Open a Terminal window. You can find it using Spotlight Search.

2. Type in hostname and hit the Return key.

In this example, the name of the computer is CAS-14175.