diff --git a/R/as.data.table.R b/R/as.data.table.R
index aeef3ab1a9..c077361be2 100644
--- a/R/as.data.table.R
+++ b/R/as.data.table.R
@@ -128,6 +128,7 @@ as.data.table.list = function(x,
   eachnrow = integer(n)          # vector of lengths of each column. may not be equal if silent repetition is required.
   eachncol = integer(n)
   missing.check.names = missing(check.names)
+  origListNames = if (missing(.named)) names(x) else NULL  # as.data.table called directly, not from inside data.table() which provides .named, #3854
   for (i in seq_len(n)) {
     xi = x[[i]]
     if (is.null(xi)) next    # eachncol already initialized to 0 by integer() above
@@ -191,6 +192,7 @@ as.data.table.list = function(x,
   if (check.names) vnames = make.names(vnames, unique=TRUE)
   setattr(ans, "names", vnames)
   setDT(ans, key=key) # copy ensured above; also, setDT handles naming
+  if (length(origListNames)==length(ans)) setattr(ans, "names", origListNames)  # PR 3854 and tests 2058.15-17
   ans
 }
 
diff --git a/R/data.table.R b/R/data.table.R
index 6664dfb8bf..790a6eb475 100644
--- a/R/data.table.R
+++ b/R/data.table.R
@@ -160,10 +160,14 @@ replace_dot_alias = function(e) {
   naturaljoin = FALSE
   names_x = names(x)
   if (missing(i) && !missing(on)) {
-    i = eval.parent(.massagei(substitute(on)))
-    if (!is.list(i) || !length(names(i)))
-      stop("When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join (i.e. join on common names) is invoked")
-    naturaljoin = TRUE
+    tt = eval.parent(.massagei(substitute(on)))
+    if (!is.list(tt) || !length(names(tt))) {
+      warning("When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join (i.e. join on common names) is invoked. Ignoring on= which is '",class(tt)[1L],"'.")
+      on = NULL
+    } else {
+      i = tt
+      naturaljoin = TRUE
+    }
   }
   if (missing(i) && missing(j)) {
     tt_isub = substitute(i)
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index eef8f7d388..2308b6dfa7 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -15154,6 +15154,16 @@ test(2058.12, cbind(first=data.table(A=1:3), second=data.table(A=4, B=5:7)),
 test(2058.13, cbind(data.table(A=1:3), second=data.table(A=4, B=5:7)),
               data.table(A=1:3, second.A=4, second.B=5:7))                      # no
 test(2058.14, cbind(data.table(A=1,B=2),3), data.table(A=1,B=2,V2=3))           # no
+L = list(1:3, 4:6)
+test(2058.15, as.data.table(L), data.table(V1=1:3, V2=4:6))                     # no
+# retain all-blank list names as batchtools relies on in reg$defs[1,job.pars], #3581
+names(L) = c("","")
+test(2058.16, as.data.table(L), setnames(data.table(1:3, 4:6),c("","")))        # no
+# retain existing duplicate and blank names of a plain-list, just as 1.12.2 did
+L = list(1:3, 4:6, 7:9, 10:12)
+names(L) = c("","foo","","foo")
+test(2058.17, as.data.table(L),
+              setnames(data.table(1:3, 4:6, 7:9, 10:12),c("","foo","","foo")))  # no
 
 # rbindlist improved error message, #3638
 DT = data.table(a=1)
@@ -15316,7 +15326,7 @@ test(2060.605, fcoalesce(NULL, "foo"), NULL) # as seen in mlr using BBmisc::coal
 # #3650 -- ensure max nrow check on CJ is applied after unique
 l = replicate(ceiling(log10(.Machine$integer.max)), rep(1L, 10L), simplify = FALSE)
 l$unique = TRUE
-test(2061, do.call(CJ, l), setkey(unique(as.data.table(head(l, -1L)))))
+test(2061, do.call(CJ, l), data.table(V1=1L, V2=1L, V3=1L, V4=1L, V5=1L, V6=1L, V7=1L, V8=1L, V9=1L, V10=1L, key=paste0("V",1:10)))
 
 # #3635, not specific to non-equi joins, but only occurs in non-equi cases.
 d1 = data.table(a = c(1L, 6L), b = c(11L, 16L))
@@ -15714,8 +15724,12 @@ X = data.table(a=1:2, b=1:2)
 test(2076.01, X[on=.(a=2:3, d=2:1)], data.table(a=2:3, b=c(2L,NA_integer_), d=2:1))
 Y = data.table(a=2:3, d=2:1)
 test(2076.02, X[on=Y], data.table(a=2:3, b=c(2L,NA_integer_), d=2:1))
-test(2076.03, X[on=3], error="When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join")
-test(2076.04, X[on=list(3)], error="When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join")
+test(2076.03, X[on=3], X,
+  warning=c("When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join.*Ignoring on= which is 'numeric'",
+            "i and j are both missing so ignoring the other arguments. This warning will be upgraded to error in future."))
+test(2076.04, X[on=list(3)], X,
+  warning=c("When on= is provided but not i=, on= must be a named list or data.table|frame, and a natural join.*Ignoring on= which is 'list'",
+            "i and j are both missing so ignoring the other arguments. This warning will be upgraded to error in future."))
 
 # gsum int64 support #1647, #3464
 if (test_bit64) {