I cannot turn off the do not disturb half moon icon. No option to turn it off in settings

You should be able to select Settings > Focus then tap Do Not Disturb. That will turn it off. If these directions are not helpful, then please come back and let us know which iPhone you have and what its iOS is.

You can read more about Do Not Disturb here:

Use Do Not Disturb with Focus on your iPhone or iPad - Apple Support

Try a Forced Restart to see if it helps:

Force restart iPhone - Apple Support

Make sure the side switch is not turned down, i.e., to Silence or DND.

Do you have Screen Time Restrictions?

Settings > Screen Time > Content & Privacy Restrictions > Do Not Disturb While Driving > Allow.

See if that helpsl