In the following XSL I use an xsl:for-each on each participant but using the 
mod operator in an xsl:if I skip every other participant.

In side the xsl:if I start a TR then apply templates to the current 
participant then apply templates to the current nodes next sibiling by using 
the following-sibling axis.

BTW does the XML really have two 'given' nodes or should the second 'given' 
node actually be 'initials'?

Anthony
<xsl:stylesheet version="1.0" 
xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
	<xsl:output method="html" encoding="UTF-8" indent="yes" />
	
	<xsl:template match="/participants">
		<table>
			<xsl:for-each select="participant">
				<xsl:if test="(position() mod 2)">
					<tr>
						<xsl:apply-templates select="." />
						<xsl:apply-templates select="following-sibling::*[1]" />
					</tr>	
				</xsl:if>
			</xsl:for-each>
		</table>
	</xsl:template>
	
	<xsl:template match="participant">
		<td>
			<xsl:value-of select="participatingEntity/associatedPerson/name/given[1]" 
/>
			<xsl:text> </xsl:text>
			<xsl:value-of select="participatingEntity/associatedPerson/name/family" />
		</td>
	</xsl:template>
	
</xsl:stylesheet>