diff --git a/lisp/international/mule-cmds.el b/lisp/international/mule-cmds.el
index 5dc3de4422..465fd1bf53 100644
--- a/lisp/international/mule-cmds.el
+++ b/lisp/international/mule-cmds.el
@@ -3083,6 +3083,43 @@ mule--ucs-names-affixation
               (list name (concat (if char (format "%c" char) " ") "\t") "")))
           names))
 
+(defun mule--ucs-names-by-code (names)
+  (let* ((codes-and-names
+          (mapcar (lambda (name) (cons (gethash name ucs-names) name)) names))
+         (sorted (sort codes-and-names (lambda (a b) (< (car a) (car b))))))
+    (mapcar #'cdr sorted)))
+
+(defun mule--ucs-names-by-group (names)
+  (let* ((names-chars
+          (mapcar (lambda (name) (cons name (gethash name ucs-names))) names))
+         (groups-names
+          (seq-group-by
+           (lambda (name-char)
+             (let ((script (aref char-script-table (cdr name-char))))
+               (if script (symbol-name script) "ungrouped")))
+           names-chars))
+         names-headers header)
+    (dolist (group groups-names)
+      (setq header t)
+      (dolist (name-char (cdr group))
+        (push (list (car name-char)
+                    (concat
+                     ;; header
+                     (if header
+                         (progn
+                           (setq header nil)
+                           (concat "\n" (propertize
+                                         (format "* %s\n" (car group))
+                                         'face 'header-line)))
+                       "")
+                     ;; prefix
+                     (if (cdr name-char) (format "%c" (cdr name-char)) " ")
+                     " ")
+                    ;; suffix
+                    "")
+              names-headers)))
+    (nreverse names-headers)))
+
 (defun char-from-name (string &optional ignore-case)
   "Return a character as a number from its Unicode name STRING.
 If optional IGNORE-CASE is non-nil, ignore case in STRING.
@@ -3104,6 +3141,15 @@ char-from-name
                                            ignore-case))
                 code)))))))
 
+(defcustom read-char-by-name-display nil
+  "How to display characters by `read-char-by-name' completion."
+  :type '(choice
+          (const :tag "Sort by character names" nil)
+          (const :tag "Sort by character codepoints" code)
+          (const :tag "Group by Unicode blocks" sections))
+  :group 'mule
+  :version "28.1")
+
 (defun read-char-by-name (prompt)
   "Read a character by its Unicode name or hex number string.
 Display PROMPT and read a string that represents a character by its
@@ -3130,8 +3176,14 @@ read-char-by-name
 	   prompt
 	   (lambda (string pred action)
 	     (if (eq action 'metadata)
-		 '(metadata
-		   (affixation-function . mule--ucs-names-affixation)
+		 `(metadata
+		   (affixation-function
+                    . ,(if (eq read-char-by-name-display 'sections)
+                           'mule--ucs-names-by-group
+                         'mule--ucs-names-affixation))
+		   (display-sort-function
+                    . ,(when (eq read-char-by-name-display 'code)
+                         'mule--ucs-names-by-code))
 		   (category . unicode-name))
 	       (complete-with-action action (ucs-names) string pred)))))
 	 (char