It can be done, but it's a little tricky. It involves creating an XML file stored in a particular way with all the required data. Try this (I'm sure there's a better way):
1. Open your Illustrator file, and open the Variables palette (Window > Variables)
2. Select the text path containing the child's first name, then in the Variables palette, choose "Make Text Dynamic". This will give you a new variable, which you can rename if you like.
3. Repeat step 2 with the text path containing the last name.
4. Click on the "Camera" icon to capture a data set (the default name will be "Data Set 1", but you can rename it if you like).
5. Go to "Save Variable Library" in the palette's menu to save an XML file.
Now, at this point, you can open the XML file in your editor of choice (notepad will work). Look for the following code (some names will be different depending on how you named everything)
Code:
<v:sampleDataSets xmlns:v="&ns_vars;" xmlns="&ns_custom;">
<v:sampleDataSet dataSetName="Names">
<Variable1>
<p>First Name</p>
</Variable1>
<Variable2>
<p>Last Name</p>
</Variable2>
</v:sampleDataSet>
</v:sampleDataSets>
The next stage is to create a <v:sampleDataSet ...> tag for each line of your tab-delimited file, and replace or append the existing tag. For example, let's say your original file looks like this:
John <tab> Smith
Jane <tab> Doe
Tom <tab> Lane
...then the portion of the XML file shown above should become:
Code:
<v:sampleDataSets xmlns:v="&ns_vars;" xmlns="&ns_custom;">
<v:sampleDataSet dataSetName="[red]Name1[/red]">
<Variable1>
<p>[blue]John[/blue]</p>
</Variable1>
<Variable2>
<p>[blue]Smith[/blue]</p>
</Variable2>
</v:sampleDataSet>
<v:sampleDataSet dataSetName="[red]Name2[/red]">
<Variable1>
<p>[blue]Jane[/blue]</p>
</Variable1>
<Variable2>
<p>[blue]Doe[/blue]</p>
</Variable2>
</v:sampleDataSet>
<v:sampleDataSet dataSetName="[red]Name3[/red]">
<Variable1>
<p>[blue]Tom[/blue]</p>
</Variable1>
<Variable2>
<p>[blue]Lane[/blue]</p>
</Variable2>
</v:sampleDataSet>
</v:sampleDataSets>
Although it looks like there is a lot of text, most of it is just repeated, so a simple Find and Replace might be enough to add in all the markup to your existing file. However, keep in mind that each line (the <v:sampleDataSet ... tag above) needs to have a unique dataSetName (in red). You might be able to add a field in a spreadsheet that numbers each line to make it unique. The original XML file also has other markup, so make sure you retain all this information and only replace the area shown.
Once you have the XML file the way you want it, go back to your Illustrator file. In the Variables palette, go to "Load Variable Library..." and pick your new XML file. Click OK when a warning about overwriting appears. Pick the first dataset from the variables palette. Now, to change your artwork to another name, simply use the arrows on the Variables palette.
As you can see, variable data in Illustrator is tricky. Using scripts, you might be able to simplify much of the work, but that's a whole new topic. Personally, I'd recommend using InDesign CS2 instead to overprint the text over your illustration. It's much easier to set up, you can use your tab-delimited file directly, and you can print all the names in one go.