The 'Profile' icon continues to display the original 'First name' from the Google account even after changes are made to the profile details

Expected behavior

Step 4: The 'Profile' icon should display the updated 'Public display name' instead of the original 'First name' from the Google email account.
Step 7: After changing the 'First name', 'Last name', and 'Public display name', the 'Profile' icon should reflect these updates accurately.

Actual behavior

Step 4: The 'Profile' icon displays the 'First name' from the Google email account.
Step 7: After changing the 'First name', 'Last name', and 'Public display name', the 'Profile' icon still displays the original 'First name' from the Google email account.

Steps to reproduce the behavior

1. Click 'Log in or sign up with WordPress.com'
2. Click 'Continue with Google'
3. Sign in with a google email
4. Click 'Me' button
5. Click 'My Profile'
6. Change the 'First name', 'Last name' and 'Public display name'
7. Click 'Back' icon

Tested on [device], Android [version], JPAndroid / WPAndroid [version]

Galaxy S21 5G, 12, Jetpack 25.2.1 (1444)/WordPress 25.2.1 (1444)

Reproduce the issue through Continue with Google, then Me > My Profile, changing the First name, Last name, and Public display name before using Back. Trace the profile icon's displayed name and verify that it reflects the updated Public display name rather than the original Google account first name.