Oh, here's another version, which is probably more what you want
(assuming the children of Members should be in the same namespace):
<?xml version="1.0"?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform";>
<xsl:output method='xml' version='1.0' encoding='utf-8' indent='yes'/>
<xsl:template match="/">
<Organization>
<xsl:apply-templates/>
</Organization>
</xsl:template>
<xsl:template match="People">
<Members xmlns="http://www.foo.com/namespace/v1";>
<xsl:apply-templates/>
</Members>
</xsl:template>
<xsl:template match="Person">
<Member xmlns="http://www.foo.com/namespace/v1";>
<xsl:value-of select="concat(substring(LName,1,1),'.',FName)"/>
</Member>
</xsl:template>
</xsl:stylesheet>