diff --git a/zerver/lib/users.py b/zerver/lib/users.py
index 7fa334c473..3b4a5070df 100644
--- a/zerver/lib/users.py
+++ b/zerver/lib/users.py
@@ -12,6 +12,8 @@ def check_full_name(full_name_raw):
     full_name = full_name_raw.strip()
     if len(full_name) > UserProfile.MAX_NAME_LENGTH:
         raise JsonableError(_("Name too long!"))
+    if len(full_name) < UserProfile.MIN_NAME_LENGTH:
+        raise JsonableError(_("Name too short!"))
     if list(set(full_name).intersection(UserProfile.NAME_INVALID_CHARS)):
         raise JsonableError(_("Invalid characters in name!"))
     return full_name
diff --git a/zerver/models.py b/zerver/models.py
index 7585dcf351..83df122b97 100644
--- a/zerver/models.py
+++ b/zerver/models.py
@@ -534,6 +534,7 @@ class UserProfile(ModelReprMixin, AbstractBaseUser, PermissionsMixin):
 
     USERNAME_FIELD = 'email'
     MAX_NAME_LENGTH = 100
+    MIN_NAME_LENGTH = 3
     API_KEY_LENGTH = 32
     NAME_INVALID_CHARS = ['*', '`', '>', '"', '@']
 
diff --git a/zerver/tests/test_bots.py b/zerver/tests/test_bots.py
index c958b8fe0e..3f1cd665b9 100644
--- a/zerver/tests/test_bots.py
+++ b/zerver/tests/test_bots.py
@@ -62,13 +62,25 @@ class BotTest(ZulipTestCase, UploadSerializeMixin):
         self.login("hamlet@zulip.com")
         self.assert_num_bots_equal(0)
         bot_info = dict(
-            full_name='',
-            short_name='',
+            full_name='My bot name',
+            short_name='@',
         )
         result = self.client_post("/json/bots", bot_info)
         self.assert_json_error(result, 'Bad name or username')
         self.assert_num_bots_equal(0)
 
+    def test_add_bot_with_no_name(self):
+        # type: () -> None
+        self.login("hamlet@zulip.com")
+        self.assert_num_bots_equal(0)
+        bot_info = dict(
+            full_name='a',
+            short_name='bot',
+        )
+        result = self.client_post("/json/bots", bot_info)
+        self.assert_json_error(result, 'Name too short!')
+        self.assert_num_bots_equal(0)
+
     def test_add_bot(self):
         # type: () -> None
         self.login("hamlet@zulip.com")
diff --git a/zerver/tests/test_settings.py b/zerver/tests/test_settings.py
index c9eeb8f629..2da7ec4912 100644
--- a/zerver/tests/test_settings.py
+++ b/zerver/tests/test_settings.py
@@ -107,6 +107,11 @@ class ChangeSettingsTest(ZulipTestCase):
                                        dict(full_name='x' * 1000))
         self.assert_json_error(json_result, 'Name too long!')
 
+        # Now try a too-short name
+        json_result = self.client_post("/json/settings/change",
+                                       dict(full_name='x'))
+        self.assert_json_error(json_result, 'Name too short!')
+
     def test_illegal_characters_in_name_changes(self):
         # type: () -> None
         email = 'hamlet@zulip.com'
diff --git a/zerver/tests/test_users.py b/zerver/tests/test_users.py
index 449026d6db..1b29b33270 100644
--- a/zerver/tests/test_users.py
+++ b/zerver/tests/test_users.py
@@ -156,6 +156,14 @@ class PermissionTest(ZulipTestCase):
         result = self.client_patch('/json/users/hamlet@zulip.com', req)
         self.assert_json_error(result, 'Name too long!')
 
+    def test_admin_cannot_set_short_full_name(self):
+        # type: () -> None
+        new_name = 'a'
+        self.login('iago@zulip.com')
+        req = dict(full_name=ujson.dumps(new_name))
+        result = self.client_patch('/json/users/hamlet@zulip.com', req)
+        self.assert_json_error(result, 'Name too short!')
+
     def test_admin_cannot_set_full_name_with_invalid_characters(self):
         # type: () -> None
         new_name = 'Opheli*'