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I have a dataset like this (reproducible)

X1 <- c(0,0,1,3)
X2 <- c(0,0,4,5)
X3 <- c(0,2,2,6)
X4 <- c(0,0,0,1)

df <- data.frame(rbind(X1, X2, X3, X4))
rownames(df) <- NULL
df

 X1 X2 X3 X4
1 0 0 1 3
2 0 0 4 5
3 0 2 2 6
4 0 0 0 1

I want to add a column, which will take the value of the column name where, per row wise, value changed from 0 to any value greater than 0

Hence expected output is

 X1 X2 X3 X4 Value
1 0 0 1 3 X3
2 0 0 4 5 X3
3 0 2 2 6 X2
4 0 0 1 1 X4

How can I achieve this for each row?

The Vectorized way to do it would be,

names(df)[max.col(df != 0, ties.method = 'first')]
#[1] "X3" "X3" "X2" "X4"

In addition, you can use apply with margin 1 (to do row operations), and find the first index where the diff is not 0, i.e.

names(df)[apply(df, 1, function(i) which(diff(i) != 0)[1]) + 1]
#[1] "X3" "X3" "X2" "X4"

Another option using apply again:

names(df)[apply(df, 1, function(x) which(x > 0)[1])]
# [1] "X3" "X3" "X2" "X4"

A tidyverse solution:

df %>%
 rowid_to_column() %>% #Creating an ID
 gather(var, val, -rowid) %>% #Transforming the data from wide to long
 arrange(rowid) %>% #Arranging according ID
 group_by(rowid) %>% #Grouping by ID
 mutate(res = ifelse(cumsum(val) > 0, paste0(var), NA)) %>% #Applying the condition
 filter(res == first(res[!is.na(res)])) %>% #Selecting the relevant value
 left_join(df %>% rowid_to_column(), by = c("rowid" = "rowid")) %>% #Joining with the original df
 ungroup() %>% 
 select(-rowid, -var, -val) #Deleting the redundant variables

 res X1 X2 X3 X4
 <chr> <dbl> <dbl> <dbl> <dbl>
1 X3 0. 0. 1. 3.
2 X3 0. 0. 4. 5.
3 X2 0. 2. 2. 6.
4 X4 0. 0. 0. 1.