Index: src/main/java/org/apache/jackrabbit/oak/query/ast/NodeLocalNameImpl.java
===================================================================
--- src/main/java/org/apache/jackrabbit/oak/query/ast/NodeLocalNameImpl.java	(revision 1668924)
+++ src/main/java/org/apache/jackrabbit/oak/query/ast/NodeLocalNameImpl.java	(working copy)
@@ -28,6 +28,7 @@
 import org.apache.jackrabbit.oak.commons.PathUtils;
 import org.apache.jackrabbit.oak.query.index.FilterImpl;
 import org.apache.jackrabbit.oak.spi.query.PropertyValues;
+import org.apache.jackrabbit.oak.spi.query.QueryConstants;
 
 /**
  * The function "localname(..)".
@@ -68,24 +69,45 @@
     @Override
     public PropertyValue currentProperty() {
         String name = PathUtils.getName(selector.currentPath());
-        int colon = name.indexOf(':');
-        // TODO LOCALNAME: evaluation of local name might not be correct
-        String localName = colon < 0 ? name : name.substring(colon + 1);
+        String localName = getLocalName(name);
         // TODO reverse namespace remapping?
         return PropertyValues.newString(localName);
     }
+    
+    static String getLocalName(String name) {
+        int colon = name.indexOf(':');
+        // TODO LOCALNAME: evaluation of local name might not be correct
+        return colon < 0 ? name : name.substring(colon + 1);
+    }
 
     @Override
     public void restrict(FilterImpl f, Operator operator, PropertyValue v) {
-        // TODO support LOCALNAME index conditions
+        if (v == null) {
+            return;
+        }
+
+        String name = NodeNameImpl.getName(query, v);
+        if (name == null) {
+            throw new IllegalArgumentException("Invalid name value: " + v.toString());
+        }
+        if (f.getSelector().equals(selector)
+                && NodeNameImpl.supportedOperator(operator)) {
+            f.restrictProperty(QueryConstants.RESTRICTION_LOCAL_NAME,
+                    operator, PropertyValues.newString(name));
+        }
     }
-    
+
     @Override
     public void restrictList(FilterImpl f, List<PropertyValue> list) {
         // optimizations of type "LOCALNAME(..) IN(A, B)" are not supported
     }
 
     @Override
+    public boolean supportsRangeConditions() {
+        return false;
+    }
+
+    @Override
     public boolean canRestrictSelector(SelectorImpl s) {
         return s.equals(selector);
     }
Index: src/main/java/org/apache/jackrabbit/oak/query/ast/NodeNameImpl.java
===================================================================
--- src/main/java/org/apache/jackrabbit/oak/query/ast/NodeNameImpl.java	(revision 1668924)
+++ src/main/java/org/apache/jackrabbit/oak/query/ast/NodeNameImpl.java	(working copy)
@@ -28,8 +28,10 @@
 import org.apache.jackrabbit.oak.api.Type;
 import org.apache.jackrabbit.oak.commons.PathUtils;
 import org.apache.jackrabbit.oak.namepath.JcrNameParser;
+import org.apache.jackrabbit.oak.query.QueryImpl;
 import org.apache.jackrabbit.oak.query.index.FilterImpl;
 import org.apache.jackrabbit.oak.spi.query.PropertyValues;
+import org.apache.jackrabbit.oak.spi.query.QueryConstants;
 import org.apache.jackrabbit.util.ISO9075;
 
 /**
@@ -86,11 +88,16 @@
         if (v == null) {
             return;
         }
-        String name = getName(v);
+        String name = getName(query, v);
         if (name == null) {
             throw new IllegalArgumentException("Invalid name value: " + v.toString());
         }
-        // TODO support NAME(..) index conditions
+        if (f.getSelector().equals(selector)
+                && NodeNameImpl.supportedOperator(operator)) {
+            String localName = NodeLocalNameImpl.getLocalName(name);
+            f.restrictProperty(QueryConstants.RESTRICTION_LOCAL_NAME,
+                    operator, PropertyValues.newString(localName));
+        }
     }
     
     @Override
@@ -110,7 +117,7 @@
      * @param v the value
      * @return name value, or {@code null} if the value can not be converted
      */
-    private String getName(PropertyValue v) {
+    static String getName(QueryImpl query, PropertyValue v) {
         // TODO correctly validate JCR names - see JCR 2.0 spec 3.2.4 Naming Restrictions
         switch (v.getType().tag()) {
         case PropertyType.DATE:
@@ -133,7 +140,11 @@
         }
         return name;
     }
-    
+
+    static boolean supportedOperator(Operator o) {
+        return o == Operator.EQUAL || o == Operator.LIKE;
+    }
+
     @Override
     int getPropertyType() {
         return PropertyType.NAME;
Index: src/main/java/org/apache/jackrabbit/oak/spi/query/QueryConstants.java
===================================================================
--- src/main/java/org/apache/jackrabbit/oak/spi/query/QueryConstants.java	(revision 0)
+++ src/main/java/org/apache/jackrabbit/oak/spi/query/QueryConstants.java	(working copy)
@@ -0,0 +1,30 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+package org.apache.jackrabbit.oak.spi.query;
+
+public abstract class QueryConstants {
+
+    /**
+     * Name of the property restriction used to express query performed
+     * via NAME and LOCALNAME functions
+     */
+    public static final String RESTRICTION_LOCAL_NAME = ":localname";
+
+}
\ No newline at end of file
Index: src/test/java/org/apache/jackrabbit/oak/query/FilterTest.java
===================================================================
--- src/test/java/org/apache/jackrabbit/oak/query/FilterTest.java	(revision 1668924)
+++ src/test/java/org/apache/jackrabbit/oak/query/FilterTest.java	(working copy)
@@ -46,6 +46,23 @@
         QueryImpl q = (QueryImpl) p.parse(sql);
         return q.createFilter(true);
     }
+    
+    private Filter createFilterSQL(String sql) throws ParseException {
+        QueryImpl q = (QueryImpl) p.parse(sql);
+        return q.createFilter(true);
+    }
+    
+    @Test
+    public void localName() throws Exception {
+        Filter f = createFilterSQL("select * from [nt:base] where localname() = 'resource'");
+        assertEquals("[resource]", f.getPropertyRestrictions(":localname").toString());
+    }
+    
+    @Test
+    public void name() throws Exception {
+        Filter f = createFilter("//*[fn:name() = 'nt:resource']");
+        assertEquals("[resource]", f.getPropertyRestrictions(":localname").toString());
+    }
 
     @Test
     public void mvp() throws Exception {