Should I change filesystem back to read only after resetting password?

I needed to reset my Ubuntu password in VM, so I booted into recovery mode, remounted the filesystem to rw, and successfully updated the password. Then I resume normal boot.

My question is, do I need to set it back to read only? Or does Ubuntu automatically restores it back to read only upon normal boot?

The only reason why you'd have a partition in read only mode is not to cause any data corruption. If you already made it read write and the partition didn't get affected by that, there's no need to set it back to read only. That is performed automatically by the OS when you initiate a system shutdown which is, again, a precaution to prevent any data loss.