If conditions and copying values from different rows

I have the following data:

Data <- data.frame(Project=c(123,123,123,123,123,123,124,124,124,124,124,125,125,125),
               Name=c("Harry","David","David","Harry","Peter","Peter","John","Alex","Alex","Mary","Mary","Dan","Joe","Joe"),
                      Value=c(1,4,7,3,8,9,8,3,2,5,6,2,2,1),
                      OldValue=c("","Open","In Progress","Complete","Open","In Progress","Complete","Open","In Progress","System Declined","In Progress","","Open","In Progress"),
                      NewValue=c("Open","In Progress","Complete","Open","In Progress","Complete","Open","In Progress","System Declined","In Progress","Complete","Open","In Progress","Complete"))

The data should look like this

I want to create another column called EditedBy that applies the following logic.

1. IF the project in row 1 equals the project in row 2 AND the New Value in row 1 equals "Open" THEN take the name from row 2. If either of the first two conditions are False, then stick with the name in the first row.

So the data should look like this

How can I do this?