A conditional formatting rule can only apply to one worksheet. So you can't have one rule that highlights duplicates in four worksheets.
You can have a rule in each worksheet that highlights cell in that worksheet that are duplicated in any of the other three. You would have to rewrite the rule in each sheet.
You have not given enough information to actually write the rules for you. "duplicate names" Which cells contain the names you want to check for duplicates? Do all sheets have identical layouts?
For example, if A1:A10 contained names on all sheets:
Applies to $A$1:$A$10
Excel Formula:
=COUNTIF(Sheet1!$A$1:$A$10,A1)+COUNTIF(Sheet2!$A$1:$A$10,A1)+COUNTIF(Sheet3!$A$1:$A$10,A1)>0
Rewrite the rule for each sheet to reference the other three.