Hi,
can you try the below:
[Is Edit Mode]&&Name==[Current User]
Edit:
I have taken a look into this for you an if you are using rules to show and hide a field I think there are 2 issues, one is the use of fn- and also you need to work in the negative.
For example, to show the field if User=Current User and form is Edit mode you need the following rule.
Assuming that 'user' is a people field.
and(not(equals(User,[Current User(Login ID)])),or([Is Display Mode],[Is New Mode]))
If the rule is to hide the control if User=Current user and form is Edit mode you need the following rule.
and(equals(User,[Current User(Login ID)]),[Is Edit Mode])
works like a charm. thanks!