Apply point-in-polygon to multiple polygons with identifier

Question

I have a dataframe with thousands of lat long along with other attributes

> head(df)
  created_on latitude longitude       day Value Order Total.Value
1    55:40.8 13.01504  80.19199  7/9/2022     2    74          19
2    08:27.0 12.97431  80.19029  7/9/2022    19    49          14
3    39:59.5 12.95778  80.19588  7/9/2022    26   205          50
4    20:43.0 13.07842  80.18144  7/8/2022     1   178           7
5    34:06.2 12.92485  80.09914 7/10/2022     7   106          12
6    08:12.1 12.88727  80.23384 7/10/2022    10   167          17

I have a few polygons in WKT format

head(Poly)

    WKT                                                                  name
1 POLYGON ((80.156 13.058, 80.156 13.040, 80.182 13.052, 80.156 13.058))  Polygon-1
2 POLYGON ((80.2015739 13.050, 80.223 13.033, 80.223 13.049, 80.201 13.050)) Polygon-2
3 POLYGON ((80.185 13.021, 80.200 13.009, 80.202 13.020, 80.185 13.021)) Polygon-3

I want to apply Point-in-Polygon to the df and identify the lat longs that lie in any of these polygons. The output should contain the original attributes of the lat longs as well as the name of the polygon in which they lie. I have been able to do it for one polygon at a time but it becomes tedious when I have up to 10-20 polygon to run through. I used the rgeos package to translate the WKT into a dataframe and the sp package to apply point in polygon). Below is the code already used

Poly <- read.csv("PIP0.csv")
str <- Poly[2,1]
test <- readWKT(str)

#convert wkt to data.frame of coordinates
coords <- as.data.frame(coordinates(test@polygons[[1]]@Polygons[[1]]))

Points <- read.csv("PIP2.csv")

#logical vector to determine whether points in the df-Point are present in Poly 
A <- as.logical(point.in.polygon(Points$latitude, Points$longitude, coords$y, coords$x, mode.checked = FALSE ))

Points$flag[A] <- "This point is present in Polygon" 

Thanks,