You mentioned in another thread that you're using Mint Mobile, which I gather uses the T-Mobile network.
While traveling abroad, I used my regular SIM and paid to have my cell service work abroad. Other networks' names appeared on my phone, just like T-Mobile is showing up on yours.
I can't say whether this is expected behavior or not, but it's not surprising. If your phone is connecting and working as expected, I wouldn't worry about it showing T-Mobile instead of Mint Mobile.