diff --git a/R/fit.R b/R/fit.R
index 55badc098..ca74aa9ec 100644
--- a/R/fit.R
+++ b/R/fit.R
@@ -265,6 +265,7 @@ fit_xy.model_spec <-
         rlang::warn(glue::glue("Engine set to `{object$engine}`."))
       }
     }
+    y_var <- colnames(y)
 
     if (object$engine != "spark" & NCOL(y) == 1 & !(is.vector(y) | is.factor(y))) {
       if (is.matrix(y)) {
@@ -278,6 +279,7 @@ fit_xy.model_spec <-
     eval_env <- rlang::env()
     eval_env$x <- x
     eval_env$y <- y
+    eval_env$y_var <- y_var
     eval_env$weights <- weights_to_numeric(case_weights, object)
 
     # TODO case weights: pass in eval_env not individual elements
diff --git a/R/fit_helpers.R b/R/fit_helpers.R
index d08aead4e..5fd9021df 100644
--- a/R/fit_helpers.R
+++ b/R/fit_helpers.R
@@ -187,11 +187,16 @@ xy_form <- function(object, env, control, ...) {
     control = control,
     ...
   )
-  if (is.vector(env$y)) {
-    data_obj$y_var <- character(0)
+  if (!is.null(env$y_var)) {
+    data_obj$y_var <- env$y_var
   } else {
+    if (is.vector(env$y)) {
+      data_obj$y_var <- character(0)
+    }
+
     data_obj$y_var <- colnames(env$y)
   }
+
   res$preproc <- data_obj[c("x_var", "y_var")]
   res
 }