@EOnegin

I just spun up a new CentOS 7 Droplet, received the root password, and logged in using:

ssh root@IP

Where IP = Droplet Public IP.

After entering in the password once more and changing it at the prompt, I was brought to the normal prompt as expected.

I’m using Terminal on my MacBook Pro, though I also tested this on Windows 10 using PuTTy w/o any issues on my end.

Have you tried simply destroying the current Droplet or recreating it? I know that doesn’t help too much, though I can’t see any issues popping up when testing on a new droplet.

Because you used simply password, try add a similar password such as the password supplied by the system. I have solved this problem with this method, and after changed successfully, you can change again with new simple password