UPDATE: Despite having put in a ticket with Visible support, I'm still showing up as "WIRELESS CALLER" on caller ID. But here is the strange thing, I popped in a physical Red Pocket sim, and the option to show caller ID worked on my iPhone. Now I'm wondering if it's an esim issue.
For me, the name of the party who previously owned the number was showing up.
I submitted a ticket to Visible asking for it to be changed to my name and about 12 hours later received an email from Visible indicating the change had been successfully completed. However, they changed it to "Wireless Caller," not my name as the initial chat agent had said he'd submit.
I just contacted chat again and was told that Visible doesn't offer "premium Caller ID services." The only options are either "Wireless Caller" or your 10-digit phone number.
Visible assigned my number. Seems they should be able to label the Caller ID, too. If I'm not in someone's contacts so my name pops up, they don't take my calls!