Other people seeing me as unknown when I call?

I have an iPhone XR with T-Mobile. Just in the last few days, when I've called my husband and sister, they've both told me I'm showing up as "unknown" to them when clearly I'm in their contacts. I did check my settings and it looks like my caller ID wasn't turned on somehow, although I haven't changed any settings myself. If I turn that on, will anyone I call see my name? If I'm calling somewhere like a business, I don't want my name to show but I assume if I toggle caller ID to "on" then that will give my name to anyone I call? I just want people who have my in their phone as a contact to see my name rather than them thinking it's not one of their contacts? But I don't know if it's an issue with my phone? Husband has TMobile but sister has Verizon so if it's a carrier issue it sends odd that both would change around the same day.