To assign custom labels to products, please follow the instructions provided
Step 1:
Go to Store Admin –> Content–> Metaobjects –> Click on “Add definition
Add metaobject definition as below and click save

In the metaobject for Product Labels, Add three distinct fields: Label, Text Color, and Background, as illustrated below.
Key must be product_labels.label, product_labels.text_color, product_labels.background for respective field



Once you done adding all three object, click on save button.
Step 2:
Click on Product Labels and add labels as reference below.
Add all badge(labels) you want to display on products. I.e. Best seller, Trending, Limited stock, New etc.

Step 3:
Go to Store Admin –> Settings–> Metafields and metaobjects–> Products -> Click on Add definition
Add definition as below.
Namespace and key : custom.select_labels

Step 4:
Now go to products, select any product, scroll down to Metafields and select entry from Select Labels

Click “Save” to view the desired labels on the products