diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
index 1229ff3c3..784935aa7 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/AbstractComposableFunctionRegistry.java
@@ -281,7 +281,7 @@ public abstract class AbstractComposableFunctionRegistry implements FunctionRegi
 		this.types.computeIfAbsent(name, str -> functionType);
 	}
 
-	private void addName(Object function, String name) {
+	protected void addName(Object function, String name) {
 		this.names.put(function, name);
 	}
 
diff --git a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalog.java b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalog.java
index 445f59229..37df46714 100644
--- a/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalog.java
+++ b/spring-cloud-function-context/src/main/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalog.java
@@ -82,6 +82,7 @@ public class InMemoryFunctionCatalog extends AbstractComposableFunctionRegistry
 
 		for (String name : functionRegistration.getNames()) {
 			addType(name, functionRegistration.getType());
+			addName(functionRegistration.getTarget(), name);
 			if (functionRegistration.getTarget() instanceof Function) {
 				this.addFunction(name, (Function<?, ?>) functionRegistration.getTarget());
 			}
diff --git a/spring-cloud-function-context/src/test/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalogTests.java b/spring-cloud-function-context/src/test/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalogTests.java
index edc5f0268..1cc47c927 100644
--- a/spring-cloud-function-context/src/test/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalogTests.java
+++ b/spring-cloud-function-context/src/test/java/org/springframework/cloud/function/context/catalog/InMemoryFunctionCatalogTests.java
@@ -18,6 +18,7 @@ package org.springframework.cloud.function.context.catalog;
 
 import java.util.function.Function;
 
+import org.junit.Ignore;
 import org.junit.Test;
 import reactor.core.publisher.Flux;
 
@@ -59,6 +60,9 @@ public class InMemoryFunctionCatalogTests {
 
 		lookedUpFunction = catalog.lookup("foo");
 		assertThat(lookedUpFunction).isNotNull();
+		assertThat(catalog.lookupFunctionName(lookedUpFunction)).isEqualTo("foo");
+		assertThat(catalog.getFunctionType("foo").getOutputType())
+				.isEqualTo(String.class);
 		assertThat(lookedUpFunction instanceof FluxFunction).isTrue();
 	}
 
@@ -87,7 +91,6 @@ public class InMemoryFunctionCatalogTests {
 		FunctionRegistration<UpperCaseMessage> upperCaseRegistration = new FunctionRegistration<>(
 				new UpperCaseMessage(), "uppercase")
 						.type(FunctionType.of(UpperCaseMessage.class).getType());
-		// TODO: make this work with plain Reverse (not message)
 		FunctionRegistration<ReverseMessage> reverseRegistration = new FunctionRegistration<>(
 				new ReverseMessage(), "reverse")
 						.type(FunctionType.of(ReverseMessage.class).getType());
@@ -95,6 +98,31 @@ public class InMemoryFunctionCatalogTests {
 		catalog.register(upperCaseRegistration);
 		catalog.register(reverseRegistration);
 
+		Function<Flux<Message<String>>, Flux<Message<String>>> lookedUpFunction = catalog
+				.lookup("uppercase|reverse");
+		assertThat(catalog.getFunctionType("uppercase|reverse").isMessage()).isTrue();
+		assertThat(catalog.lookupFunctionName(lookedUpFunction))
+				.isEqualTo("uppercase|reverse");
+
+		assertThat(lookedUpFunction).isNotNull();
+		assertThat(lookedUpFunction
+				.apply(Flux.just(MessageBuilder.withPayload("star").build())).blockFirst()
+				.getPayload()).isEqualTo("RATS");
+	}
+
+	@Test
+	@Ignore
+	public void testFunctionCompositionMixedMessages() {
+		FunctionRegistration<UpperCaseMessage> upperCaseRegistration = new FunctionRegistration<>(
+				new UpperCaseMessage(), "uppercase")
+						.type(FunctionType.of(UpperCaseMessage.class).getType());
+		// TODO: make this work with plain Reverse (not message)
+		FunctionRegistration<Reverse> reverseRegistration = new FunctionRegistration<>(
+				new Reverse(), "reverse").type(FunctionType.of(Reverse.class).getType());
+		InMemoryFunctionCatalog catalog = new InMemoryFunctionCatalog();
+		catalog.register(upperCaseRegistration);
+		catalog.register(reverseRegistration);
+
 		Function<Flux<Message<String>>, Flux<Message<String>>> lookedUpFunction = catalog
 				.lookup("uppercase|reverse");
 		assertThat(catalog.getFunctionType("uppercase|reverse").isMessage()).isTrue();