First, we used a super-tiny end mill (0.020 inches in diameter!) to engrave her name in a piece of acrylic.

Then we created a base from polyethylene. While it machines OK, it absolutely sucks to cut on the bandsaw (it just melts against the blade). It was so bad, I ended up using the mill to "cut" the piece from a larger block. Here, we've added an LED. This one is a green (because she likes green, of course) Avago 1W LED. We put one at each end facing towards the center where her name will go.

Here's a test of the unit. The green LEDs shine into the acrylic, and where it hits the engraving, it comes out the front. The picture is a little over-exposed. It looks way nicer in real life.
We tucked all the wiring into the base and added a barrel plug in the back that hooks up to a miscellaneous DC "wall-wart" I had laying around. The barrel plug fit nicely into the hole we machined into the base, and there was a slot in the bottom for all of the wires and a resistor (to limit the current to the LEDs). The wires and resistor were kept securely in the base using H.G. technology (that's Hot Glue, for the unacronymned).