I hacked it, though I didn't understand everything that I did.
I noticed pryr::address was giving a different kind of results than tracemem and tried it (I had to dig into the code to use pryr:::address2 because pryr::address doesn't have an environment argument). 
Then I noticed that mixing the results from tracemem on x and pryr:::address2 on the rest of the objects there was a match (after basic reformatting) :
`(<-` <- function(x,value){
  pf <- parent.frame()
  all_addresses       <- sapply(ls(pf), pryr:::address2, pf)
  all_addresses       <- all_addresses[names(all_addresses) != "*tmp*"]
  all_addresses_short <- gsub("(^|<)[0x]*(.*?)(>|$)","\\2",all_addresses)
  x_address       <- tracemem(x)
  x_address_short <- tolower(gsub("(^|<)[0x]*(.*?)(>|$)","\\2",x_address))
  ind    <- match(x_address_short, all_addresses_short)
  x_name <- names(all_addresses)[ind]
  message("all_addresses, using pryr::address2")
  print(all_addresses)
  print(all_addresses_short)
  message("x_address, using tracemem")
  print(x_address)
  print(x_address_short)
  message("x_name, matching substrings")
  print(x_name)
  value
}
The regex used in gsub calls tries to account for the address formats we get with different systems, I'm not 100% sure that it's general.
output:
foo <- 1
bar <- 2
(foo) <- foo
# all_addresses, using pryr::address2
# (<-          bar          foo 
# "0x1433df50" "0x14937678" "0x14937708" 
# (<-        bar        foo 
# "1433df50" "14937678" "14937708" 
# x_address, using tracemem
# [1] "<0000000014937708>"
# [1] "14937708"
# x_name, matching substrings
# [1] "foo"
It breaks if x is not a variable name, for example:
foo <- iris
(foo$species) <- 3
We could assume that if the address isn't found x is a list item, and then lookup its address among the addresses of the items of all the lists we have in the parent.frame (recursively), but I think that's enough ugly hacks for today.