Assuming an XSLT 2.0 processor like Saxon 9 or XmlPrime or Altova Raptor you can do it with
Code:
<xsl:stylesheet
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
exclude-result-prefixes="xs"
version="2.0">
<xsl:template match="@* | node()">
<xsl:copy>
<xsl:apply-templates select="@* | node()"/>
</xsl:copy>
</xsl:template>
<xsl:template match="Member">
<xsl:copy>
<xsl:apply-templates select="@*"/>
<xsl:attribute name="fullPath" select="ancestor::*/@name" separator="."/>
<xsl:apply-templates/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>