MacOS makes it easy to change the name of your Mac in Airdrop.
Just follow the following 4 steps and you'll be golden.
Step 1: Open your System Preferences
The fastest way to open your settings is by typing ⌘ + space, then "pref" and choosing "System Preferences" from the dropdown menu.
Step 2: Click the Sharing icon
It's the folder with the yellow diamond on it. I pointed to it below for your convenience.
Step 3: Edit the Computer Name
You will see your computer name at the top, and can click into the text field to update it.
Once you've changed it to whatever name you want, you just need to click Edit.
Step 4: Confirm your new computer name
Now you can just click the "OK button." Your settings will be saved.
Your AirDrop name is now updated.
You can close out of System Preferences.
Now when people see you on AirDrop, they'll see your new AirDrop name.