How to match column names across two dataframes and add a new variable?

data <- rbind(c(1,2,3,4,5,6),
              c(1,2,3,4,5,6),
              c(1,2,3,4,5,6))

colnames(data) <- c("A", "B", "C", "D", "E", "F")

category_vector <- cbind(c("A", "B", "C", "D", "E"),
                         c("Cat1", "Cat2", "Cat3", "Cat2", "Cat5"))
colnames(category_vector) <- c("Name", "Category")

My goal is to match column names in data, to the names in category_vector and then assign each column of data the corresponding category name in Row 1.

My desired output is as follows:

output <- rbind(c("Cat1", "Cat2", "Cat3", "Cat2", "Cat5", "NA"),
                c(1,2,3,4,5,6),
                c(1,2,3,4,5,6),
                c(1,2,3,4,5,6))
colnames(output) <- colnames(data)

I know, that I can use match(names(x), names(y)) to show the intersect, but I am not sure how to get to the desired output.

Here is one example:

library(dplyr)

data <- rbind(c(1,2,3,4,5,6),
             c(1,2,3,4,5,6),
             c(1,2,3,4,5,6))

colnames(data) <- c("A", "B", "C", "D", "E", "F")

category_vector <- cbind(c("A", "B", "C", "D", "E"),
                         c("Cat1", "Cat2", "Cat3", "Cat2", "Cat5"))

#colnames(category_vector) <- c("Name", "Category")

# turn everything in data into a character
data <- data |> 
    as.data.frame() |> 
    mutate(across(everything(), as.character))

category_vector <- as.data.frame(t(category_vector))

names(category_vector) <- category_vector[1, ]

category_vector <- category_vector[-1, ]

category_vector |> 
    bind_rows(data)

     A    B    C    D    E    F
1 Cat1 Cat2 Cat3 Cat2 Cat5 <NA>
2    1    2    3    4    5    6
3    1    2    3    4    5    6
4    1    2    3    4    5    6