Here’s a simple stylesheet that checks whether an ID is within an approved list of IDs and uses a “display name” for it in the output.
<?xml version="1.0"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="2.0">
<xsl:variable name="desired-ids">
<id name="rd_bl">Red to Blue</id>
<id name="pu_gr">Purple to Green</id>
</xsl:variable>
<xsl:template match="root">
<root>
<xsl:apply-templates />
</root>
</xsl:template>
<xsl:template match="DATA">
<xsl:variable name="current-id" select="ID/text()" />
<xsl:if test="$desired-ids/id[@name=$current-id]">
<entry>
<name>
<xsl:value-of select="$desired-ids/id[@name=$current-id]" />
</name>
<travel>
<xsl:value-of select="travel" />
</travel>
<delay>
<xsl:value-of select="delay" />
</delay>
</entry>
</xsl:if>
</xsl:template>
</xsl:stylesheet>
Output using your example XML after correcting the closing tag errors:
<root>
<entry>
<name>Red to Blue</name>
<travel>15</travel>
<delay>7</delay>
</entry>
<entry>
<name>Purple to Green</name>
<travel>17</travel>
<delay>6</delay>
</entry>
</root>
EDIT: in case you’re stuck with XSL 1.0:
<?xml version="1.0"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="1.0">
<xsl:variable name="desired-ids">rd_bl="Red to Blue" pu_gr="Purple to Green"</xsl:variable>
<xsl:template match="root">
<root>
<xsl:apply-templates />
</root>
</xsl:template>
<xsl:template match="DATA">
<xsl:variable name="current-id" select="ID/text()" />
<xsl:variable name="id-with-equals" select="concat($current-id, '=')" />
<xsl:if test="contains($desired-ids, $id-with-equals)">
<xsl:variable name="id-with-open-quote" select="concat($id-with-equals, '"')" />
<xsl:variable name="display-name" select="substring-before(substring-after($desired-ids, $id-with-open-quote), '"')" />
<entry>
<name>
<xsl:value-of select="$display-name" />
</name>
<travel>
<xsl:value-of select="travel" />
</travel>
<delay>
<xsl:value-of select="delay" />
</delay>
</entry>
</xsl:if>
</xsl:template>
</xsl:stylesheet>
You can see this is much less elegant, it uses awkward string-matching to check for a valid ID and extract the display name.