XSLT to duplicate elements with different a different attribute

I need to create an XSLT transform to go from

Input

<pizza>
    <pref name="cheese_cheddar" value="2" />
    <pref name="meat_chicken" value="5" />
    <pref name="cheese_edam" value="10" />
</pizza>

to, Output

<pizza>
    <pref name="cheese_cheddar" value="2" />
    <pref name="tasty_cheese_cheddar" value="2" />
    <pref name="meat_chicken" value="5" />
    <pref name="cheese_edam" value="10" />
    <pref name="tasty_cheese_edam" value="10" />
</pizza>

That is, all elements inside pizza that start with cheese_ need to be duplicated with the name element modified to append to word tasty_.

I've got a matcher working, <xsl:template match="node()[starts-with(@name, 'slippage_')]"> but I've no clue how to duplicate elements and modify an attribute. I've not done XSLT work before so I'm not sure if copy and copy-to are appropriate for duplicating elements with different attributes.