Change my iCloud password

Yes it is absolutely possible and intended IF YOU SHARE AN APPLE ID with someone else. IF you are in doubt then change the password to your Apple ID. Below is how you can do this-

Open Settings ➔ Apple ID (Your Name at Top) ➔ Password & Security ➔ Change Password.

Axel F.

If the other phone is logged in to the same Apple ID, then yes. Apple IDs are personal, and should not be shared any more than you would share a toothbrush. Not only are messages shared, so is everything else; photos, calendars, reminders, contacts...

You can see what other devices are sharing your Apple ID by going to Settings, tapping on your name at the top, and then looking at the list of devices near the bottom of the page.