For your app to come up in the list, you will need to have an intent filter for a unique data type. If multiple apps are capable of handling the same data, your app might not show, but a list will come up with your app and any other app that has the same filter.
Usually none of the default apps have intent filter for name mimetype. So by adding below intent filter your app will show up. But it is always preferable if you mention the right data so that your app will show up only for data that is present in the Contact.
Whatsapp and Skype implement their own custom Mimetype and add this data to each Contact. You might have to do the same thing , if there are multiple apps that handle name mimetype
<intent-filter>
<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.DEFAULT" />
<data android:mimeType="vnd.android.cursor.item/name" />
</intent-filter>