diff --git a/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/HoverInfoProvider.java b/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/HoverInfoProvider.java
index e8a5247e86..c98a0437d1 100644
--- a/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/HoverInfoProvider.java
+++ b/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/HoverInfoProvider.java
@@ -15,7 +15,6 @@
 import java.util.LinkedList;
 import java.util.List;
 import java.util.Optional;
-import java.util.stream.Stream;
 
 import org.eclipse.core.runtime.CoreException;
 import org.eclipse.core.runtime.IPath;
@@ -101,33 +100,11 @@ public List<Either<String, MarkedString>> computeHover(int line, int column, IPr
 			if (monitor.isCanceled()) {
 				return cancelled(res);
 			}
-			IJavaElement[] elements = JDTUtils.findElementsAtSelection(unit, line, column, this.preferenceManager, monitor);
-			if (elements == null || elements.length == 0 || monitor.isCanceled()) {
-				return cancelled(res);
-			}
-			IJavaElement curr = null;
-			if (elements.length != 1) {
-				// they could be package fragments.
-				// We need to select the one that matches the package fragment of the current unit
-				IPackageFragment packageFragment = (IPackageFragment) unit.getParent();
-				IJavaElement found =
-						Stream
-						.of(elements)
-						.filter(e -> e.equals(packageFragment))
-						.findFirst()
-						.orElse(null);
-				if (found == null) {
-					// this would be a binary package fragment
-					curr = elements[0];
-				} else {
-					curr = found;
-				}
-			} else {
-				curr = elements[0];
-			}
-			if (monitor.isCanceled()) {
+			IJavaElement curr = JDTUtils.findElementAtSelection(unit, line, column, this.preferenceManager, monitor);
+			if (curr == null || monitor.isCanceled()) {
 				return cancelled(res);
 			}
+
 			if (JDTEnvironmentUtils.isSyntaxServer() || isResolved(curr, monitor)) {
 				IBuffer buffer = curr.getOpenable().getBuffer();
 				if (buffer == null && curr instanceof BinaryMember binaryMember) {
diff --git a/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/JDTUtils.java b/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/JDTUtils.java
index d5c384fdb5..7ac861399e 100644
--- a/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/JDTUtils.java
+++ b/org.eclipse.jdt.ls.core/src/org/eclipse/jdt/ls/core/internal/JDTUtils.java
@@ -1078,10 +1078,32 @@ public static IJavaElement findElementAtSelection(ITypeRoot unit, int line, int
 		if (monitor.isCanceled()) {
 			return null;
 		}
-		if (elements != null && elements.length == 1) {
+		if (elements == null || elements.length == 0) {
+			return null;
+		}
+		if (elements.length == 1) {
 			return elements[0];
 		}
-		return null;
+		return resolveElementAtSelection(unit, line, column, elements);
+	}
+
+	/**
+	 * When multiple elements are at the same position, returns the one whose name matches
+	 * the identifier at the cursor. Works for any element type (packages, modules, types, etc.).
+	 */
+	private static IJavaElement resolveElementAtSelection(ITypeRoot unit, int line, int column, IJavaElement[] elements) throws JavaModelException {
+		IBuffer buffer = unit.getBuffer();
+		if (buffer != null) {
+			String identifier = getIdentifierAt(buffer, line, column);
+			if (identifier != null) {
+				for (IJavaElement e : elements) {
+					if (identifier.equals(e.getElementName())) {
+						return e;
+					}
+				}
+			}
+		}
+		return elements[0];
 	}
 
 	public static IJavaElement[] findElementsAtSelection(ITypeRoot unit, int line, int column, PreferenceManager preferenceManager, IProgressMonitor monitor) throws JavaModelException {
@@ -1109,6 +1131,41 @@ public static IJavaElement[] findElementsAtSelection(ITypeRoot unit, int line, i
 		return null;
 	}
 
+	/**
+	 * Returns the identifier at the given position in the buffer, including dots (e.g. for module names like "java.xml").
+	 * Used when multiple elements are at the same position (e.g. JEP 511 module imports) to pick the one matching the source.
+	 *
+	 * @param buffer the buffer, or null
+	 * @param line 0-based line
+	 * @param column 0-based column
+	 * @return the identifier at position, or null if none or buffer is null
+	 */
+	public static String getIdentifierAt(IBuffer buffer, int line, int column) {
+		if (buffer == null) {
+			return null;
+		}
+		int offset = JsonRpcHelpers.toOffset(buffer, line, column);
+		if (offset < 0 || offset >= buffer.getLength()) {
+			return null;
+		}
+		int start = offset;
+		while (start > 0 && isIdentifierPart(buffer.getChar(start - 1))) {
+			start--;
+		}
+		int end = offset;
+		while (end < buffer.getLength() && isIdentifierPart(buffer.getChar(end))) {
+			end++;
+		}
+		if (start >= end) {
+			return null;
+		}
+		return buffer.getText(start, end - start);
+	}
+
+	private static boolean isIdentifierPart(char c) {
+		return Character.isLetterOrDigit(c) || c == '_' || c == '.';
+	}
+
 	public static boolean isSameParameters(IMethod method1, IMethod method2) {
 		if (method1 == null || method2 == null) {
 			return false;