Hello there Tinybubbles,
Thanks for posting here on the Apple Support Communities!
We understand you're having some issues with your Apple ID on your iPhone after changing your Apple ID and password. Typically, when you see your name grayed out in Settings, this indicates restrictions are present on the device. Let's explore that first: Use parental controls on your child's iPhone, iPad, and iPod touch
- Go to Settings > Screen Time > Content & Privacy Restrictions.
- Swipe up until you see the 'Allow Changes' section.
- Make sure 'Account Changes' is set to Allow. If you see 'Don't Allow', then tap on it to change it to Allow.
Then, you'll find the best steps to follow in this next article, for what to do after you change your Apple ID and password: What to do after you change your Apple ID or password
We hope this helps get you pointed in the right direction.
Take care.