renaming specific columns in a data frame in R

I am trying to change the names of specific columns of a data frame in R. for example, If i have a data frame that looks something like this:

df <- data.frame(
x1 = rnorm(10),
y1 = rnorm(10),
x2 = rnorm(10),
y2 = rnorm(10),
x3 = rnorm(10),
y3 = rnorm(10)
)
head(df,3)

           x1          y1         x2          y2         x3         y3
1 -1.42423743  0.21855807 -0.1456853  1.46204179  1.6474040  2.2384782
2  1.17158831 -1.41602524 -1.2891551  1.45028848 -1.2726250 -0.3331051
3 -0.21959357  0.84741665  0.2745170  0.81040227 -0.3520883 -0.3103068

What I want to do is change the names of all the y columns (i.e., y1, y2, y3) to just simply y. So the resulting data frame would look like this:

           x1           y         x2           y         x3          y
1 -1.42423743  0.21855807 -0.1456853  1.46204179  1.6474040  2.2384782
2  1.17158831 -1.41602524 -1.2891551  1.45028848 -1.2726250 -0.3331051
3 -0.21959357  0.84741665  0.2745170  0.81040227 -0.3520883 -0.3103068

I realise there's now multiple y-columns in the data frame, but for my purposes it's necessary.

Im not sure how to do this, but I was thinking of looping through the df and changing the column names... this code doesn't work, but I was thinking of something like this:

for(j in 1:length(df)){
  colnames(df$[j])[which(names(df$[j]) == "y[j]")] <- "y"
} 

Any suggestion as to how I'd achieve this?