Q: Change iCloud login info on iPhone

Hello there, pdxphotos.

It sounds like you are trying to sign-out of iCloud to login with a different or current account. To sign out of iCloud, this Knowledge Base article offers the steps to follow:

Sign in with a different Apple ID on your iPhone, iPad, or iPod touch

Your Apple ID is the account you use to access Apple services like the App Store, Apple Music, iCloud, iMessage, FaceTime and more. It includes the email address and password you use to sign in as well as all the contact, payment, and security details you'll use across Apple services. You can sign in to all Apple services with a single Apple ID and password. 

If you're no longer using the email address associated with your Apple ID, you can change the email address that you use as your Apple ID, then use the steps below to update it in the services on your device. If you forgot your Apple ID, there are a few ways to find it.

iCloud

1. Tap Settings > iCloud on your iOS device. If you see the option to sign in, you can change your Apple ID now.
2. Scroll down and tap Sign Out. 
   
3. Tap Sign Out again to confirm. After you sign out of iCloud, you might not be able to access some of your data that's stored in iCloud until you sign in again. If you're part of a family, you need to sign back in to use Family Sharing.
4. Choose Keep on My iPhone or Delete from My iPhone when you're asked what you want to do with your iCloud data. 
5. Enter your password to sign out. 
6. Go to Settings > iCloud and enter your Apple ID and password.
7. Tap Sign In.

If you updated your Apple ID email address and your device repeatedly asks for the password to your previous Apple ID, you can temporarily change your Apple ID to sign in.

If what you are trying to do is change your Apple ID to reflect a more current email then this article provides insight and links to the steps for changing your Apple ID:

About your Apple ID email addresses

Email addresses you use with your Apple ID

Your Apple ID uses email addresses to sign you in to your account with Apple. With your Apple ID, you can access services like the App Store, Apple Music, iCloud, iMessage, FaceTime, and more. We'll use your email addresses to send you information about your account, and to help friends and family communicate and share with you.

Apple ID email address
This is the email address you use with your password when signing in to any Apple service. It’s also the primary email address on your account.
 

Additional email addresses
Add extra email addresses to your account to help people find you on Apple services like FaceTime, iMessage, Game Center, and Find My Friends.
 

Rescue email address
You have the option to add a rescue email address to your account for more security. You can see it when you sign in to your Apple ID account page.

Before you can use a new or updated Apple ID, we'll send you a verification email to make sure the email address belongs to you.

Apple ID email address

When you create an Apple ID, you enter an email address. This email address is your Apple ID and the username that you'll use to sign in to Apple services like iTunes and iCloud. It's also the contact email address for your account. Be sure to check your email address regularly. We'll send you email notifications to help you manage your account and make the most of your Apple ID.

Follow these steps to change your Apple ID.

Thanks for participating in Apple Support Communities.

Cheers.