How to use custom ISP Name?

For example, my school uses a local county agency for internet access, which uses Verizon's backbone- but still identifies itself as the name of the county program. What do ISP's use to identify themselves when you connect? If I were to start a small project in my community with multiple internet lines, how could I identify the name of our business (like when online services detect your ISP) instead of the company we used for the internet access?