Tom,
I'm assuming you are drilling with a drill press and not by hand.
Drilling acrylics is somewhat more delicate than drilling wood, It's rather prone to heat.
So, very small bites, clearing the swarf frequently. You can use brad point wood drills stopping just as the point breaks
through the bottom but NO MORE,
then either turn the blank upside down and drill through the last bit or cut off the last millimeter or so by hand,
Alternatively using machine drills, measuring again carefully and marking the drill so you stop drilling before breaking through the bottom,
again cutting off that last bit by hand.
If it's a slimline type pen needing a 7mm drill it's no problem using that size drill bit.
If however it's a large type pen when the need is for a 13.1mm or so drill, I find starting with a smaller diameter drill bit advantageous.
When it's glued up you should square the end until the brass tube shows with an appropriate sized end mill, (best on the drill press)
I know some pen makers square the blank end using jigs on a disk sander but IMO an end mill is best.
Don't get put off with early failures, all pen makers break something or other some time.
Best of luck, don't forget pics of your first pen good or just good.
John. B
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