Select polygon by clicking on map, changing item selected via dropdown

Thanks @jlacko I have changed it to use leaflet and now it prints the NAME upon clicking on the map. Do you know how I can change the dropdown to be the same as what is selected in the map?

library(shiny)
library(sf)
library(tidyverse)
library(leaflet)

# data in the sf package
nc <- st_read(system.file("shape/nc.shp", package="sf")) %>% 
    select(NAME, AREA)

# unique names
nc_names <- nc %>% 
    st_set_geometry(NULL) %>% 
    distinct(NAME) %>%
    pull()

# Define UI for application that draws a histogram
ui <- fluidPage(    
    # Generate a row with a sidebar
    sidebarLayout(      
        # Define the sidebar with one input
        sidebarPanel(
            selectInput("name",
                        "name",
                        nc_names
            )
        ),
        # Create a spot for the barplot
        mainPanel(
            mainPanel(leafletOutput("map") )
        )
    )
)

server <- function(input, output) {
    
    # filter polygon for map based on location selected
    shp_selected <- reactive({
        req(input$name)
        nc %>% filter(NAME == input$name)       
    })
    
    output$map <- renderLeaflet({
        leaflet() %>% 
            addProviderTiles("Stamen.TonerHybrid") %>% 
            addPolygons(data = nc, 
                        fillColor = NULL, 
                        color = "grey",
                        weight = 0.1,
                        layerId = ~NAME) %>% 
            addPolygons(data = shp_selected(), 
                        fillColor = "blue", 
                        color = "grey",
                        fillOpacity = 0.5,
                        layerId = ~NAME)
        
    })
    
    #click on polygon
    observe({ 
        event <- input$map_shape_click
        print(event$id)
        
    })
    
    # map selection - not sure if this is the way to do it - still needs to be assigned to be the same as the dropdown
    output$map_selection <- reactive({
        req(event$id)
        event$id
    })
    
}

shinyApp(ui, server)