You can use whatever name you want to process credit cards. Some banks will ask you to file a DBA which is very inexpensive to do.
So, You can have a company called : MyComapny LLC
You can have a merchant account that processes credit cards under the name Super Service.
What shows up on your customer's statement is called a Descriptor.
You can get multiple descriptors depending on the bank. I have worked with a single business that had over 50 descriptors based on their products. Sometimes this makes great sense because if you bulk all your businesses in one portfolio you will qualify for great processing rates, the drawback is that negative charge-backs affects all the businesses.
I would recommend you speak with someone that is really connected with merchant accounts.
I always go out of my way to recommend Kirk McWorther from Flag Ship Merchant Services. They do a kick ass job for startups, and will support you as you grow.
best of luck.