use string content of a variable to refer to a column in a dataframe using transmute dplyr

I would suggest using !! from rlang and as.name(). These two elements are useful for the kind of evaluation you want in order to create your variables:

#Data
test1 <- data.frame(a = 1:5, b = 6:10)
#Var name
second_column = "b"
#Data 2
test2 <- test1 %>% 
  transmute(variable1 = a,
            variable2 = !!as.name(second_column)
  )
#Dataframes
test1
test2

Output:

test1

  a  b
1 1  6
2 2  7
3 3  8
4 4  9
5 5 10

test2

  variable1 variable2
1         1         6
2         2         7
3         3         8
4         4         9
5         5        10