diff --git a/src/ClientTlsContext.php b/src/ClientTlsContext.php
index 7dc6182..6724542 100644
--- a/src/ClientTlsContext.php
+++ b/src/ClientTlsContext.php
@@ -22,6 +22,8 @@ final class ClientTlsContext
 
     private bool $verifyPeer = true;
 
+    private bool $verifyPeerName = true;
+
     private int $verifyDepth = 10;
 
     private ?array $peerFingerprint = null;
@@ -127,6 +129,8 @@ public function withoutPeerVerification(): self
     {
         $clone = clone $this;
         $clone->verifyPeer = false;
+        // This is for compatibility with the former behaviour:
+        $clone->verifyPeerName = false;
 
         return $clone;
     }
@@ -139,6 +143,40 @@ public function hasPeerVerification(): bool
         return $this->verifyPeer;
     }
 
+    /**
+     * Enable peer name verification, this is the default with verifyPeer enabled.
+     *
+     * @return self Cloned, modified instance.
+     */
+    public function withPeerNameVerification(): self
+    {
+        $clone = clone $this;
+        $clone->verifyPeerName = true;
+
+        return $clone;
+    }
+
+    /**
+     * Disable peer name verification.
+     *
+     * @return self Cloned, modified instance.
+     */
+    public function withoutPeerNameVerification(): self
+    {
+        $clone = clone $this;
+        $clone->verifyPeerName = false;
+
+        return $clone;
+    }
+
+    /**
+     * @return bool Whether peer verification is enabled.
+     */
+    public function hasPeerNameVerification(): bool
+    {
+        return $this->verifyPeerName;
+    }
+
     /**
      * Maximum chain length the peer might present including the certificates in the local trust store.
      *
@@ -452,7 +490,7 @@ public function toStreamContextArray(): array
             'crypto_method' => $this->toStreamCryptoMethod(),
             'peer_name' => $this->peerName,
             'verify_peer' => $this->verifyPeer,
-            'verify_peer_name' => $this->verifyPeer,
+            'verify_peer_name' => $this->verifyPeerName,
             'verify_depth' => $this->verifyDepth,
             'ciphers' => $this->ciphers ?? \OPENSSL_DEFAULT_STREAM_CIPHERS,
             'capture_peer_cert' => $this->capturePeer,
diff --git a/src/ServerTlsContext.php b/src/ServerTlsContext.php
index 46da393..eeec1b7 100644
--- a/src/ServerTlsContext.php
+++ b/src/ServerTlsContext.php
@@ -58,6 +58,8 @@ public static function fromServerResource($socket): ?self
 
     private bool $verifyPeer = false;
 
+    private bool $verifyPeerName = true;
+
     private int $verifyDepth = 10;
 
     private ?string $ciphers = null;
@@ -166,6 +168,40 @@ public function hasPeerVerification(): bool
         return $this->verifyPeer;
     }
 
+    /**
+     * Enable peer name verification, this is the default with verifyPeer enabled.
+     *
+     * @return self Cloned, modified instance.
+     */
+    public function withPeerNameVerification(): self
+    {
+        $clone = clone $this;
+        $clone->verifyPeerName = true;
+
+        return $clone;
+    }
+
+    /**
+     * Disable peer name verification.
+     *
+     * @return self Cloned, modified instance.
+     */
+    public function withoutPeerNameVerification(): self
+    {
+        $clone = clone $this;
+        $clone->verifyPeerName = false;
+
+        return $clone;
+    }
+
+    /**
+     * @return bool Whether peer verification is enabled.
+     */
+    public function hasPeerNameVerification(): bool
+    {
+        return $this->verifyPeer && $this->verifyPeerName;
+    }
+
     /**
      * Maximum chain length the peer might present including the certificates in the local trust store.
      *
@@ -437,7 +473,7 @@ public function toStreamContextArray(): array
             'crypto_method' => $this->toStreamCryptoMethod(),
             'peer_name' => $this->peerName,
             'verify_peer' => $this->verifyPeer,
-            'verify_peer_name' => $this->verifyPeer,
+            'verify_peer_name' => $this->verifyPeer && $this->verifyPeerName,
             'verify_depth' => $this->verifyDepth,
             'ciphers' => $this->ciphers ?? \OPENSSL_DEFAULT_STREAM_CIPHERS,
             'honor_cipher_order' => true,
diff --git a/test/ClientTlsContextTest.php b/test/ClientTlsContextTest.php
index be70b34..258dca6 100644
--- a/test/ClientTlsContextTest.php
+++ b/test/ClientTlsContextTest.php
@@ -85,6 +85,31 @@ public function testWithoutPeerVerification(): void
         self::assertFalse($clonedContext->hasPeerVerification());
     }
 
+    public function testDefaultPeerNameVerification(): void
+    {
+        $context = new ClientTlsContext;
+        self::assertTrue($context->hasPeerNameVerification());
+    }
+
+    public function testWithoutPeerNameVerification(): void
+    {
+        $context = new ClientTlsContext;
+        $clonedContext = $context->withPeerVerification()->withoutPeerNameVerification();
+
+        self::assertTrue($clonedContext->hasPeerVerification());
+        self::assertFalse($clonedContext->hasPeerNameVerification());
+    }
+
+    public function testContextOptionsWithoutPeerNameVerification(): void
+    {
+        $context = new ClientTlsContext;
+        $clonedContext = $context->withPeerVerification()->withoutPeerNameVerification();
+        $options = $clonedContext->toStreamContextArray()['ssl'];
+
+        self::assertTrue($options['verify_peer']);
+        self::assertFalse($options['verify_peer_name']);
+    }
+
     public function certificateDataProvider(): array
     {
         return [
diff --git a/test/ServerTlsContextTest.php b/test/ServerTlsContextTest.php
index 0d74413..7b6d9d3 100644
--- a/test/ServerTlsContextTest.php
+++ b/test/ServerTlsContextTest.php
@@ -85,6 +85,31 @@ public function testWithoutPeerVerification(): void
         self::assertFalse($clonedContext->hasPeerVerification());
     }
 
+    public function testDefaultPeerNameVerification(): void
+    {
+        $context = new ServerTlsContext;
+        self::assertFalse($context->hasPeerNameVerification());
+    }
+
+    public function testWithoutPeerNameVerification(): void
+    {
+        $context = new ServerTlsContext;
+        $clonedContext = $context->withPeerVerification()->withoutPeerNameVerification();
+
+        self::assertTrue($clonedContext->hasPeerVerification());
+        self::assertFalse($clonedContext->hasPeerNameVerification());
+    }
+
+    public function testContextOptionsWithoutPeerNameVerification(): void
+    {
+        $context = new ServerTlsContext;
+        $clonedContext = $context->withPeerVerification()->withoutPeerNameVerification();
+        $options = $clonedContext->toStreamContextArray()['ssl'];
+
+        self::assertTrue($options['verify_peer']);
+        self::assertFalse($options['verify_peer_name']);
+    }
+
     public function verifyDepthDataProvider(): array
     {
         return [