Function to change names of variables in R

I have a data set that has a poor naming convention in it and I'm struggling to find a way to automate the name changing process. An example of the data is shown below:

x1 <- rnorm(10)
x2 <- rnorm(10)
y  <- rnorm(10)
x11 <- rnorm(10)
x3 <- rnorm(10)
y1 <- rnorm(10)
x21 <- rnorm(10)
x31 <- rnorm(10)

data <- data.frame(x1, x2, y, x11, x3, y1, x21, x31)
head(data,2)

This outputs a data frame that looks like this:

          x1         x2          y        x11          x3         y1
1 -0.9071106  0.6852567  0.7185932 -0.1943458  1.71832739  0.1568951
2 -0.4592129 -0.3567014 -0.3137624  0.9683101 -0.15601160  0.8513820

         x21        x31
1  0.6160399 -1.3877095
2 -1.0286380 -1.6583842

What I'm trying to do is change the name of each x-column to the to the first number that appears beside the x. For example, column x11 should just read x1... and column x21 should be just x2. I could achieve this by manually changing each name by doing something like this:

names(data)[startsWith(names(data), "y")] <- "y"
names(data)[startsWith(names(data), "x1")] <- "x1"
names(data)[startsWith(names(data), "x2")] <- "x2"
names(data)[startsWith(names(data), "x3")] <- "x3"

head(data,2)

Which outputs:

          x1         x2          y         x1         x3         y
1 -0.9071106  0.6852567  0.7185932 -0.1943458  1.7183274 0.1568951
2 -0.4592129 -0.3567014 -0.3137624  0.9683101 -0.1560116 0.8513820
          x2        x3
1  0.6160399 -1.387709
2 -1.0286380 -1.658384

But I'm struggling to write a function to do this over the entire dataset. Also, I realise that this will result in having multiple x1, x2 (etc) columns... but for my purposes, I need the data like this.

Any suggestions as to how id write this function?