What business name my customers see on their bank or credit card statement?

Your customer will see "Statement   descriptor " name in their statement which you had provided in your Stripe Account Settings.  

# Follow below steps to change / update your statement descriptor:

Step 1: Login to your Stripe account

Step 2: Tap on Settings-> Account Information  

Step 3: Find   Statement descriptor' field and insert the descriptor which you would like to appear on your customers' bank statement.

Step 4: Tap on Save button.