map over and change column names from a data frame

I have a data frame and a list. The list consists of 12 lists and the data frame consists of 12 rows and 2 columns. How can I map over the lists and change each of the list column names according to the data frame?.

That is, the data frame looks like:

           Var1         Var2
1   Sepal.Width Sepal.Length
2  Petal.Length Sepal.Length
3   Petal.Width Sepal.Length

The lists look like:

[[1]]
# A tibble: 2 x 2
      x     y
  <dbl> <dbl>
1   2     2  
2   3.8   3.8

[[2]]
# A tibble: 2 x 2
      x     y
  <dbl> <dbl>
1   3     3  
2   6.9   6.9

[[3]]
# A tibble: 2 x 2
      x     y
  <dbl> <dbl>
1   1     1  
2   2.5   2.5

The expected output

[[1]]
# A tibble: 2 x 2
Sepal.Width Sepal.Length
  <dbl> <dbl>
1   2     2  
2   3.8   3.8

[[2]]
# A tibble: 2 x 2
Petal.Length Sepal.Length
  <dbl> <dbl>
1   3     3  
2   6.9   6.9

[[3]]
# A tibble: 2 x 2
Petal.Width Sepal.Length
  <dbl> <dbl>
1   1     1  
2   2.5   2.5

Where now the column names of each of the lists are labeled according to the data frame.

Data

var_lists <- list(structure(list(x = c(2, 3.8), y = c(2, 3.8)), row.names = c(NA, 
-2L), class = c("tbl_df", "tbl", "data.frame")), structure(list(
    x = c(3, 6.9), y = c(3, 6.9)), row.names = c(NA, -2L), class = c("tbl_df", 
"tbl", "data.frame")), structure(list(x = c(1, 2.5), y = c(1, 
2.5)), row.names = c(NA, -2L), class = c("tbl_df", "tbl", "data.frame"
)), structure(list(x = c(4.9, 7.9), y = c(4.9, 7.9)), row.names = c(NA, 
-2L), class = c("tbl_df", "tbl", "data.frame")), structure(list(
    x = c(3, 6.9), y = c(3, 6.9)), row.names = c(NA, -2L), class = c("tbl_df", 
"tbl", "data.frame")), structure(list(x = c(1, 2.5), y = c(1, 
2.5)), row.names = c(NA, -2L), class = c("tbl_df", "tbl", "data.frame"
)), structure(list(x = c(4.9, 7.9), y = c(4.9, 7.9)), row.names = c(NA, 
-2L), class = c("tbl_df", "tbl", "data.frame")), structure(list(
    x = c(2, 3.8), y = c(2, 3.8)), row.names = c(NA, -2L), class = c("tbl_df", 
"tbl", "data.frame")), structure(list(x = c(1, 2.5), y = c(1, 
2.5)), row.names = c(NA, -2L), class = c("tbl_df", "tbl", "data.frame"
)), structure(list(x = c(4.9, 7.9), y = c(4.9, 7.9)), row.names = c(NA, 
-2L), class = c("tbl_df", "tbl", "data.frame")), structure(list(
    x = c(2, 3.8), y = c(2, 3.8)), row.names = c(NA, -2L), class = c("tbl_df", 
"tbl", "data.frame")), structure(list(x = c(3, 6.9), y = c(3, 
6.9)), row.names = c(NA, -2L), class = c("tbl_df", "tbl", "data.frame"
)))

var_combos <- structure(list(Var1 = structure(c(2L, 3L, 4L, 1L, 3L, 4L, 1L, 
2L, 4L, 1L, 2L, 3L), .Label = c("Sepal.Length", "Sepal.Width", 
"Petal.Length", "Petal.Width"), class = "factor"), Var2 = structure(c(1L, 
1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L), .Label = c("Sepal.Length", 
"Sepal.Width", "Petal.Length", "Petal.Width"), class = "factor")), out.attrs = list(
    dim = c(4L, 4L), dimnames = list(Var1 = c("Var1=Sepal.Length", 
    "Var1=Sepal.Width", "Var1=Petal.Length", "Var1=Petal.Width"
    ), Var2 = c("Var2=Sepal.Length", "Var2=Sepal.Width", "Var2=Petal.Length", 
    "Var2=Petal.Width"))), class = "data.frame", row.names = c(NA, 
-12L))