diff --git a/etc/NEWS b/etc/NEWS
index fb77688470..ed04bcdf13 100644
--- a/etc/NEWS
+++ b/etc/NEWS
@@ -851,6 +851,16 @@ iso-transl RET', it supports the same key sequences as 'C-x 8',
 so e.g. like 'C-x 8 [' inserts a left single quotation mark,
 'C-x \ [' does the same.
 
+---
+*** New user option 'read-char-by-name-sort'.
+It can enable sorting the characters of completion from
+'C-x 8 RET TAB' by codepoints instead of character names.
+
+---
+*** New user option 'read-char-by-name-group'.
+It groups the characters of completion from 'C-x 8 RET TAB'
+by Unicode blocks.
+
 ---
 *** Improved language transliteration in Malayalam input methods.
 Added a new Mozhi scheme.  The inapplicable ITRANS scheme is now
diff --git a/lisp/international/mule-cmds.el b/lisp/international/mule-cmds.el
index 5dc3de4422..0df410987e 100644
--- a/lisp/international/mule-cmds.el
+++ b/lisp/international/mule-cmds.el
@@ -3083,6 +3083,42 @@ mule--ucs-names-affixation
               (list name (concat (if char (format "%c" char) " ") "\t") "")))
           names))
 
+(defun mule--ucs-names-group (names)
+  (let* ((codes-and-names
+          (mapcar (lambda (name) (cons (gethash name ucs-names) name)) names))
+         (grouped
+          (seq-group-by
+           (lambda (code-name)
+             (let ((script (aref char-script-table (car code-name))))
+               (if script (symbol-name script) "ungrouped")))
+           codes-and-names))
+         names-with-header header)
+    (dolist (group (sort grouped (lambda (a b) (string< (car a) (car b)))))
+      (setq header t)
+      (dolist (code-name (cdr group))
+        (push (list
+               (cdr code-name)
+               (concat
+                (if header
+                    (progn
+                      (setq header nil)
+                      (concat "\n" (propertize
+                                    (format "* %s\n" (car group))
+                                    'face 'header-line)))
+                  "")
+                ;; prefix
+                (if (car code-name) (format "%c" (car code-name)) " ") "\t")
+               ;; suffix
+               "")
+              names-with-header)))
+    (nreverse names-with-header)))
+
+(defun mule--ucs-names-sort-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 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 +3140,22 @@ char-from-name
                                            ignore-case))
                 code)))))))
 
+(defcustom read-char-by-name-sort nil
+  "How to sort characters for `read-char-by-name' completion."
+  :type '(choice
+          (const :tag "Sort by character names" nil)
+          (const :tag "Sort by character codepoints" code))
+  :group 'mule
+  :version "28.1")
+
+(defcustom read-char-by-name-group nil
+  "How to group characters for `read-char-by-name' completion.
+When non-nil, split characters to sections of Unicode blocks
+sorted alphabetically."
+  :type 'boolean
+  :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 +3182,14 @@ read-char-by-name
 	   prompt
 	   (lambda (string pred action)
 	     (if (eq action 'metadata)
-		 '(metadata
-		   (affixation-function . mule--ucs-names-affixation)
+		 `(metadata
+		   (affixation-function
+                    . ,(if read-char-by-name-group
+                           'mule--ucs-names-group
+                         'mule--ucs-names-affixation))
+		   (display-sort-function
+                    . ,(when (eq read-char-by-name-sort 'code)
+                         'mule--ucs-names-sort-by-code))
 		   (category . unicode-name))
 	       (complete-with-action action (ucs-names) string pred)))))
 	 (char