Not "out of the box" .. You have to account for it.  For example.. Assume you you want to mask a person's social security number (SSN).. you can have a visible SSN field.. and a hidden SSN filed.  On the visible.. have a trigger after update that copies the clear text values to the hidden field.. and then replaces the visible values with **** .. 

It seems like you want to hide/show the "old one" field.

Assuming the "new one" is a formula field, try making it a button as follows:

1. create a new text field named toggle
2. type the letter x in the toggle field
3. set the "Default value" property of the toggle field to x
4. set the "Display field only, if" property of the toggle field to null
5. set the "Display field only, if" property of "old one" text field to:
  toggle = "x"
6. set the "On click" property of "new one" formula field to:
  if toggle = "x" then toggle := "" else toggle := "x" end

Good evening try to put 1=0 in the "Display Field Only, If" of the Old Name. As 1 is not equal to 0 then the Old Name field will not be displayed