Resampling multilevel data by group

Question

I am trying to write a function that resamples names nested in groups. My function works for resampling without respect to groups, but I don't want to create samples of names that aren't in the same group.

Here's the function, where x is a vector of all names (some repeated), a is a vector of unique name observations, and b is a vector of unique names in randomized order.

    rep <- function(x,a,b){
      for(i in 1:length(a)){
        x1 <- x
        x1[which(x==a[i])] <- b[i]
      }
      x1
    }

x <- c("Smith", "Jones", "Washington", "Miller", "Wells", "Smith", "Smith", "Miller")
a <- sort(unique(x))
b <- sample(a, length(a))

dat <- rep(x, a, b)
View(dat)
"Smith"      "Jones"      "Washington" "Miller"     "Jones"      "Smith"      "Smith"       "Miller" 

However, each name is nested in a group, so I need to avoid creating samples of names that are not in the same group. For example:

x         groupid
Smith       A1
Jones       B1
Washington  C1
Miller      A2
Wells       B1
Smith       A2
Smith       A3
Miller      A3

How can I account for that?