diff --git a/src/lib/core/fiber.c b/src/lib/core/fiber.c
index ada7972cbd6ce77eee84c09f83beb15d8959b3be..5389ce46785b8f15413cb48c51f4d2feb1f426e7 100644
--- a/src/lib/core/fiber.c
+++ b/src/lib/core/fiber.c
@@ -912,8 +912,27 @@ fiber_loop(MAYBE_UNUSED void *data)
 void
 fiber_set_name(struct fiber *fiber, const char *name)
 {
-	assert(name != NULL);
-	snprintf(fiber->name, sizeof(fiber->name), "%s", name);
+	size_t size = strlen(name) + 1;
+	if (size <= FIBER_NAME_INLINE) {
+		if (fiber->name != fiber->inline_name) {
+			free(fiber->name);
+			fiber->name = fiber->inline_name;
+		}
+	} else {
+		if (size > FIBER_NAME_MAX)
+			size = FIBER_NAME_MAX;
+		char *new_name;
+		if (fiber->name != fiber->inline_name)
+			new_name = realloc(fiber->name, size);
+		else
+			new_name = malloc(size);
+		if (new_name == NULL)
+			panic("fiber_set_name() failed with OOM");
+		fiber->name = new_name;
+	}
+	--size;
+	memcpy(fiber->name, name, size);
+	fiber->name[size] = 0;
 }
 
 static inline void *
@@ -1242,6 +1261,9 @@ fiber_destroy(struct cord *cord, struct fiber *f)
 	region_destroy(&f->gc);
 	fiber_stack_destroy(f, &cord->slabc);
 	diag_destroy(&f->diag);
+	if (f->name != f->inline_name)
+		free(f->name);
+	f->name = NULL;
 }
 
 void
@@ -1357,6 +1379,7 @@ cord_create(struct cord *cord, const char *name)
 	fiber_reset(&cord->sched);
 	diag_create(&cord->sched.diag);
 	region_create(&cord->sched.gc, &cord->slabc);
+	cord->sched.name = NULL;
 	fiber_set_name(&cord->sched, "sched");
 	cord->fiber = &cord->sched;
 
@@ -1405,6 +1428,8 @@ cord_destroy(struct cord *cord)
 	}
 	region_destroy(&cord->sched.gc);
 	diag_destroy(&cord->sched.diag);
+	if (cord->sched.name != cord->sched.inline_name)
+		free(cord->sched.name);
 	slab_cache_destroy(&cord->slabc);
 }
 
diff --git a/src/lib/core/fiber.h b/src/lib/core/fiber.h
index 8a3e5aef5c8cb78d66eb5678e8ce9e59d6470f55..cd9346a558cdd6fcd55dce6055e0a1805c87791a 100644
--- a/src/lib/core/fiber.h
+++ b/src/lib/core/fiber.h
@@ -111,7 +111,11 @@ struct cpu_stat {
 
 #endif /* ENABLE_FIBER_TOP */
 
-enum { FIBER_NAME_MAX = 32 };
+enum {
+	/** Both limits include terminating 0. */
+	FIBER_NAME_INLINE = 40,
+	FIBER_NAME_MAX = 256
+};
 
 /**
  * Fiber ids [0; 100] are reserved.
@@ -510,7 +514,12 @@ struct fiber {
 	struct ipc_wait_pad *wait_pad;
 	/** Exception which caused this fiber's death. */
 	struct diag diag;
-	char name[FIBER_NAME_MAX + 1];
+	/**
+	 * Name points at inline_name in case it is short. Long
+	 * name is allocated on the heap.
+	 */
+	char *name;
+	char inline_name[FIBER_NAME_INLINE];
 };
 
 /** Invoke on_stop triggers and delete them. */
@@ -578,7 +587,7 @@ struct cord {
 	struct slab_cache slabc;
 	/** The "main" fiber of this cord, the scheduler. */
 	struct fiber sched;
-	char name[FIBER_NAME_MAX];
+	char name[FIBER_NAME_INLINE];
 };
 
 extern __thread struct cord *cord_ptr;
diff --git a/src/lua/fiber.c b/src/lua/fiber.c
index 575a020d0519a98b64efc5bdefc9afc10874af91..330eb7e54315164fac28c9c3e7cb75e40ec14908 100644
--- a/src/lua/fiber.c
+++ b/src/lua/fiber.c
@@ -582,16 +582,16 @@ lbox_fiber_name(struct lua_State *L)
 	if (top == name_index || top == opts_index) {
 		/* Set name. */
 		const char *name = luaL_checkstring(L, name_index);
-		int name_len = strlen(name);
+		int name_size = strlen(name) + 1;
 		if (top == opts_index && lua_istable(L, opts_index)) {
 			lua_getfield(L, opts_index, "truncate");
 			/* Truncate the name if needed. */
 			if (lua_isboolean(L, -1) && lua_toboolean(L, -1) &&
-			    name_len > FIBER_NAME_MAX)
-				name_len = FIBER_NAME_MAX;
+			    name_size > FIBER_NAME_MAX)
+				name_size = FIBER_NAME_MAX;
 			lua_pop(L, 1);
 		}
-		if (name_len > FIBER_NAME_MAX)
+		if (name_size > FIBER_NAME_MAX)
 			luaL_error(L, "Fiber name is too long");
 		fiber_set_name(f, name);
 		return 0;
diff --git a/test/app/fiber.result b/test/app/fiber.result
index 6d9604ad84a5672275fdf2083204d69d086790a3..7331f61b35b9046faea714850eff1627dc4ade5b 100644
--- a/test/app/fiber.result
+++ b/test/app/fiber.result
@@ -1186,7 +1186,7 @@ fiber = nil
 ---
 ...
 --
--- gh-2622, gh-4011: fiber.name() truncates new name.
+-- gh-2622, gh-4011, gh-4394: fiber.name() truncates new name.
 --
 fiber = require('fiber')
 ---
@@ -1214,14 +1214,14 @@ fiber.name(long_name, {truncate = true})
 ...
 fiber.name()
 ---
-- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
+- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
 ...
 f = fiber.self()
 ---
 ...
 fiber.name(f)
 ---
-- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
+- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
 ...
 fiber.name(f, 'new_name')
 ---
@@ -1239,7 +1239,7 @@ fiber.name(f, long_name, {truncate = true})
 ...
 fiber.name(f)
 ---
-- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
+- aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
 ...
 --
 -- gh-3493 fiber.create() does not roll back memtx transaction
diff --git a/test/app/fiber.test.lua b/test/app/fiber.test.lua
index 6df210d9c88cbfdf0972bc5f90070480b5e6a1be..b8e9abc6e44652003f7e0a10b1926cb71af281cc 100644
--- a/test/app/fiber.test.lua
+++ b/test/app/fiber.test.lua
@@ -504,7 +504,7 @@ test_run:cmd("setopt delimiter ''");
 fiber = nil
 
 --
--- gh-2622, gh-4011: fiber.name() truncates new name.
+-- gh-2622, gh-4011, gh-4394: fiber.name() truncates new name.
 --
 fiber = require('fiber')
 long_name = string.rep('a', 300)
diff --git a/test/unit/fiber.cc b/test/unit/fiber.cc
index 91f7d43f931b1658c6480bf75df72baa391ced2a..b0dfc9b1410dccda04b9f70a12dd94ee3115816e 100644
--- a/test/unit/fiber.cc
+++ b/test/unit/fiber.cc
@@ -171,9 +171,9 @@ fiber_name_test()
 
 	note("set new fiber name: %s.\n", fiber_name(fiber()));
 
-	const char *long_name = "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"
-		"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"\
-		"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa";
+	char long_name[FIBER_NAME_MAX + 30];
+	memset(long_name, 'a', sizeof(long_name));
+	long_name[sizeof(long_name) - 1] = 0;
 
 	fiber_set_name(fiber(), long_name);
 
diff --git a/test/unit/fiber.result b/test/unit/fiber.result
index 7c9f85dcd3fd05e97798299fb29afa075a7f14c5..a61e0a2b836a25d836dbcf6183b272caa60f8385 100644
--- a/test/unit/fiber.result
+++ b/test/unit/fiber.result
@@ -5,7 +5,7 @@ SystemError Failed to allocate 42 bytes in allocator for exception: Cannot alloc
 
 # set new fiber name: Horace.
 
-# fiber name is truncated: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.
+# fiber name is truncated: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.
 
 	*** fiber_name_test: done ***
 	*** fiber_join_test ***