I had tried using your code:

  <xsl:template match="*[@type='ObjectLink']">
    <xsl:copy>
      <xsl:apply-templates
        select=
        "
          //excel_database[@id=current()/text()]/@name
        "/>
    </xsl:copy>
  </xsl:template>

which works perfectly for the certain xml file I was talking about.

I also tried using it for another one:

<?xml version="1.0" encoding="UTF-8"?>
<EnCapta>
 <Document type="Part" id=":1170780883:1282681815:" name="New
Document" >
  <FileName>\New Document</FileName>
  <Unit/>
  <ApplicationData id=":1170780887:48766733:" name="HierarchyApp" >
   <ApplicationReference id_ref=":21339045:1265399:" >
    <Name>HierarchyApp</Name>
    <MajorVersion>0</MajorVersion>
    <MinorVersion>0</MinorVersion>
   </ApplicationReference>
   <Colors template_id=":234334:9087980:" id=":1170780887:2185726:"
name="Colors Galore!" >
    <Name type="FixedString" >Colors Galore!</Name>
    <Index type="Real" >0</Index>
   </Colors>
   <Blue template_id=":0:534:" id=":1170780890:1627341938:" name="I'm
Blue" >
    <Name type="FixedString" >I'm Blue</Name>
    <Index type="Real" >0</Index>
    <Parent type="ObjectLink" >:1170780887:2185726:</Parent>
   </Blue>
   <Green template_id=":12045115:5403534:" id=":
1170780894:1308108165:" name="I'm Green" >
    <Name type="FixedString" >I'm Green</Name>
    <Index type="Real" >0</Index>
    <Parent type="ObjectLink" >:1170780887:2185726:</Parent>
   </Green>
   <Red template_id=":120045115:534:" id=":1170780900:313735256:"
name="I'm Red" >
    <Name type="FixedString" >I'm Red</Name>
    <Index type="Real" >0</Index>
    <Parent type="ObjectLink" >:1170780887:2185726:</Parent>
   </Red>
   <Link_Hierarchy template_id=":120888115:534:" id=":
1170780904:1346796842:" name="Link_Hierarchy" >
    <Root type="ObjectLink" >:1170780900:313735256:</Root>
   </Link_Hierarchy>
   <Portal_Hierarchy template_id=":177778115:534:" id=":
1170780908:132006292:" name="Portal_Hierarchy" >
    <Root type="ObjectLink" >:1170780887:2185726:</Root>
   </Portal_Hierarchy>
  </ApplicationData>
 </Document>
</EnCapta>

and reworked the code as this:

   <xsl:template match="*[@type='ObjectLink']">
    <xsl:copy>
      <xsl:apply-templates
        select="//*[@id=current()/text()]/@name"/>
    </xsl:copy>
  </xsl:template>

However, nothing is copied into the ObjectLinks.

Am I wrong on using * as a wildcard?