Hello Bcanner55,
Thank you for posting on Apple Support Communities.
What you are describing is correct, your name will show up when sharing an iCloud links because it is the name located in your iCloud settings. The only way to go around that would be to change your name from the settings of your device.
Simply go to Settings - Your name - Name, phone numbers, email - Name, and change your name to hide your last name or use a nickname, perhaps.
Using a nickname is a good way to protect your privacy and remain anonymous, if that is what you'd like to do.
Additionally, if your friends and family use iCloud as well, you can create a Shared Album and include only the people you want so that your privacy remains protected while still sharing photos. Click here to learn how: How to share albums in Photos on your iPhone, iPad, and Mac.
Hope this information helps!