diff --git a/R/data.table.R b/R/data.table.R
index a8498899f5..5ad0292329 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -2430,9 +2430,9 @@ setnames = function(x,old,new,skip_absent=FALSE) {
     if (length(old) != ncol) stop("Can't assign ",length(old)," names to a ",ncol," column data.table")
     if (anyNA(names(x))) {
       # if x somehow has some NA names, which() needs help to return them, #2475
-      w = which((names(x) != old) | (is.na(names(x)) & !is.na(old)))
+      w = which((names(x) != old) | (Encoding(names(x)) != Encoding(old)) | (is.na(names(x)) & !is.na(old)))
     } else {
-      w = which(names(x) != old)
+      w = which(names(x) != old | (Encoding(names(x)) != Encoding(old)))
     }
     if (!length(w)) return(invisible(x))  # no changes
     new = old[w]
@@ -2462,7 +2462,7 @@ setnames = function(x,old,new,skip_absent=FALSE) {
         }
       }
     }
-    if (any(w <- new==names(x)[i])) {
+    if (any(w <- new==names(x)[i] & Encoding(new)==Encoding(names(x)[i]))) {
       w = which(!w)
       new = new[w]
       i = i[w]
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 2f47209ffb..3f51783957 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -16054,7 +16054,19 @@ test(2110.2, chmatchdup(c(utf8, utf8), latin1), out)
 test(2110.3, chmatchdup(c(latin1, latin1), latin1), out)
 test(2110.4, chmatchdup(c(utf8, utf8), utf8), out)
 
+# setnames: names with same content but different encoding is considered as non-equal, #3845
+utf8 = c("\u00e7ile", "\u00de")
+latin1 = iconv(utf8, from = "UTF-8", to = "latin1")
+tbl = as.data.table(setNames(list(1, 2), latin1))
+test(2111.01, Encoding(names(tbl)), c('latin1', 'latin1'))
+setnames(tbl, utf8)
+test(2111.02, Encoding(names(tbl)), c('UTF-8', 'UTF-8'))
+setnames(tbl, 1:2, latin1)
+test(2111.03, Encoding(names(tbl)), c('latin1', 'latin1'))
+setnames(tbl, latin1, utf8)
+test(2111.04, Encoding(names(tbl)), c('UTF-8', 'UTF-8'))
+
+
 ###################################
 #  Add new tests above this line  #
 ###################################
-