In the Android Gmail app, when you have several email accounts configured, you can switch between these in the menu to the left. Any IMAP account you add, you can assign a name to. When you add a google account, it assigns the email address (e.g. firstname.lastname@example.org) as the name by default. I'm wondering if I can change that name to e.g. "Personal" or "School", etc.
I just tried it out and it seems like this is not possible.
However, did you know that you can use aliases for your Gmail Account? If your address is for instance "email@example.com", you can also use "firstname.lastname@example.org" or "email@example.com", and all E-mails will land in the same inbox. Then you can filter them by recipient-address, to gain order.
I can also recommend you the "INBOX" app by google, if you want your inbox to be more structured. Hope it helped you in any way.