You may follow the below guide to add new brand name. (NOTE: this sample is refer from another website so the content will be different from your website)
Step 1: Navigate to Stores > Attributes > Product
Step 2: Click on the brands item to edit
Step 3: Scroll to the bottom until see add option button. Click Add Option button, fill in the name and click Save Attribute to apply the changes. After that you are require to flush Magento cache in order the setting to apply.
Go to product page and check the Brand options
