Update a Value in One Column Based on Criteria in Other Columns

by 
df <- data.frame(Name=c('John Smith', 'John Smith', 'Jeff Smith'),
                 State=c('MI','WI','WI'), stringsAsFactors=F)

df <- within(df, Name[Name == 'John Smith' & State == 'WI'] <- 'John Smith1')

> df
         Name State
1  John Smith    MI
2 John Smith1    WI
3  Jeff Smith    WI

** Edit **

Edited to add that you can put whatever you like in the within expression:

df <- within(df, {
    f <- Name == 'John Smith' & State == 'WI'
    Name[f] <- 'John Smith1'
    State[f] <- 'CA'
})

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