diff --git a/spring-boot-project/spring-boot-testcontainers/src/main/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactory.java b/spring-boot-project/spring-boot-testcontainers/src/main/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactory.java
index b4bb38e17e..1e8e0d24ac 100644
--- a/spring-boot-project/spring-boot-testcontainers/src/main/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactory.java
+++ b/spring-boot-project/spring-boot-testcontainers/src/main/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactory.java
@@ -17,6 +17,7 @@
 package org.springframework.boot.testcontainers.service.connection;
 
 import java.util.Arrays;
+import java.util.List;
 import java.util.stream.Stream;
 
 import org.apache.commons.logging.Log;
@@ -61,7 +62,7 @@ public abstract class ContainerConnectionDetailsFactory<C extends Container<?>,
 	 */
 	protected static final String ANY_CONNECTION_NAME = null;
 
-	private final String connectionName;
+	private final List<String> connectionNames;
 
 	private final String[] requiredClassNames;
 
@@ -80,7 +81,19 @@ public abstract class ContainerConnectionDetailsFactory<C extends Container<?>,
 	 * @param requiredClassNames the names of classes that must be present
 	 */
 	protected ContainerConnectionDetailsFactory(String connectionName, String... requiredClassNames) {
-		this.connectionName = connectionName;
+		this(Arrays.asList(connectionName), requiredClassNames);
+	}
+
+	/**
+	 * Create a new {@link ContainerConnectionDetailsFactory} instance with the given
+	 * supported connection names.
+	 * @param connectionNames the supported connection names
+	 * @param requiredClassNames the names of classes that must be present
+	 * @since 3.4.0
+	 */
+	protected ContainerConnectionDetailsFactory(List<String> connectionNames, String... requiredClassNames) {
+		Assert.notEmpty(connectionNames, "ConnectionNames must contain at least one name");
+		this.connectionNames = connectionNames;
 		this.requiredClassNames = requiredClassNames;
 	}
 
@@ -93,8 +106,10 @@ public abstract class ContainerConnectionDetailsFactory<C extends Container<?>,
 			Class<?>[] generics = resolveGenerics();
 			Class<?> containerType = generics[0];
 			Class<?> connectionDetailsType = generics[1];
-			if (source.accepts(this.connectionName, containerType, connectionDetailsType)) {
-				return getContainerConnectionDetails(source);
+			for (String connectionName : this.connectionNames) {
+				if (source.accepts(connectionName, containerType, connectionDetailsType)) {
+					return getContainerConnectionDetails(source);
+				}
 			}
 		}
 		catch (NoClassDefFoundError ex) {
diff --git a/spring-boot-project/spring-boot-testcontainers/src/test/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactoryTests.java b/spring-boot-project/spring-boot-testcontainers/src/test/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactoryTests.java
index 09594242d7..f5cc2b4e28 100644
--- a/spring-boot-project/spring-boot-testcontainers/src/test/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactoryTests.java
+++ b/spring-boot-project/spring-boot-testcontainers/src/test/java/org/springframework/boot/testcontainers/service/connection/ContainerConnectionDetailsFactoryTests.java
@@ -16,6 +16,8 @@
 
 package org.springframework.boot.testcontainers.service.connection;
 
+import java.util.Collections;
+import java.util.List;
 import java.util.Map;
 
 import org.junit.jupiter.api.BeforeEach;
@@ -34,6 +36,7 @@ import org.springframework.context.ApplicationContext;
 import org.springframework.core.annotation.MergedAnnotation;
 
 import static org.assertj.core.api.Assertions.assertThat;
+import static org.assertj.core.api.Assertions.assertThatIllegalArgumentException;
 import static org.assertj.core.api.Assertions.assertThatIllegalStateException;
 import static org.mockito.ArgumentMatchers.any;
 import static org.mockito.BDDMockito.then;
@@ -83,6 +86,14 @@ class ContainerConnectionDetailsFactoryTests {
 		assertThat(connectionDetails).isNotNull();
 	}
 
+	@Test
+	void getConnectionDetailsWhenTypesMatchAndNameRestrictionsMatchReturnsDetails() {
+		TestContainerConnectionDetailsFactory factory = new TestContainerConnectionDetailsFactory(
+				List.of("notmyname", "myname"));
+		ConnectionDetails connectionDetails = getConnectionDetails(factory, this.source);
+		assertThat(connectionDetails).isNotNull();
+	}
+
 	@Test
 	void getConnectionDetailsWhenTypesMatchAndNameRestrictionDoesNotMatchReturnsNull() {
 		TestContainerConnectionDetailsFactory factory = new TestContainerConnectionDetailsFactory("notmyname");
@@ -90,6 +101,14 @@ class ContainerConnectionDetailsFactoryTests {
 		assertThat(connectionDetails).isNull();
 	}
 
+	@Test
+	void getConnectionDetailsWhenTypesMatchAndNameRestrictionsDoNotMatchReturnsNull() {
+		TestContainerConnectionDetailsFactory factory = new TestContainerConnectionDetailsFactory(
+				List.of("notmyname", "alsonotmyname"));
+		ConnectionDetails connectionDetails = getConnectionDetails(factory, this.source);
+		assertThat(connectionDetails).isNull();
+	}
+
 	@Test
 	void getConnectionDetailsWhenContainerTypeDoesNotMatchReturnsNull() {
 		ElasticsearchContainer container = mock(ElasticsearchContainer.class);
@@ -126,6 +145,18 @@ class ContainerConnectionDetailsFactoryTests {
 		then(context).should().publishEvent(any(BeforeTestcontainerUsedEvent.class));
 	}
 
+	@Test
+	void creatingFactoryWithEmptyNamesThrows() {
+		assertThatIllegalArgumentException()
+			.isThrownBy(() -> new TestContainerConnectionDetailsFactory(Collections.emptyList()));
+	}
+
+	@Test
+	void creatingFactoryWithNullNamesThrows() {
+		assertThatIllegalArgumentException()
+			.isThrownBy(() -> new TestContainerConnectionDetailsFactory((List<String>) null));
+	}
+
 	@SuppressWarnings({ "rawtypes", "unchecked" })
 	private TestContainerConnectionDetails getConnectionDetails(ConnectionDetailsFactory<?, ?> factory,
 			ContainerConnectionSource<?> source) {
@@ -146,6 +177,10 @@ class ContainerConnectionDetailsFactoryTests {
 			super(connectionName);
 		}
 
+		TestContainerConnectionDetailsFactory(List<String> connectionNames) {
+			super(connectionNames);
+		}
+
 		@Override
 		protected JdbcConnectionDetails getContainerConnectionDetails(
 				ContainerConnectionSource<JdbcDatabaseContainer<?>> source) {