Someone’s old Apple ID is on my iPhone somehow

When exactly do you see this? Where do you see it? What messages do you see when this happens? Worst case scenario is your phone was bought used, not signed out from Find My, and is now useless unless you know the owner of the ID. Less serious scenario is somebody else signed in on your phone, bought an app, and you just have to delete the app and download it under your ID.

'Activation Lock for iPhone, iPad, and iPod touch' is a security feature that's designed to prevent anyone else from using an iPhone, iPad, or iPod touch, if it's ever lost or stolen. To learn more click here --> http://support.apple.com/HT201365

For an individual to remove an activation lock absolutely requires the information for the account that applied the lock. Click on this link to learn 'How to remove Activation Lock' --> https://support.apple.com/HT201441

If you do not know the required information and you are not the original owner, get the owner of the account to remove the lock or return the device for a refund or recycle the device. The device is otherwise useless to you. If the owner is unknown and has not provided contact information as a message showing in the login screen, there is no way to contact the owner unless the person who gave you the device knows them.