I have a bench-top pillar drill (only I call it a drill press) that has a 2" throw. That is theoretically all that I need for some pens, but the reality is that you need more than 2" to center the bit, and then drill all the way through the blank leaving a clean bottom hole. And some pen kits require blankds longer than 2". I use a jorgensen clamp as a vise to hold the blank, drill the hole partway through the blank, and then elevate the drill table enough to finish the hole.
You can buy special purpose pen drilling jaws for some chucks.
But if you can't find pen drilling jaws for your chuck (or if you are as cheap as I am), another solution is to put the blank between centers, and turn a short tenon on one end. You don't have to turn the entire blank round - just turn the end until you have a round tenon with distinct shoulders. Then, mount the blank in a standard scroll chuck - you can use pin jaws, or you can use standard 50mm jaws by gripping the tenon at the center of the jaws rather than on the noses.
If the blank is truly square, you don't actually need to turn the tenon - just mount the blank in your chuck making sure that each of the faces of the blank is tight against one of the jaws of your chuck. However, that approach may not work as well if the blank is rectangular rather than square. You may be able to center the hole initially, but if the cross section is rectangular, it will only be held in the chuck on two faces, which means that it could slip laterally as you are drilling leaving you with an off-center hole.
I've been making wooden bodies for inexpensive Bic biro refills recently; drilling the blank is challenging because the hole is very deep (5") and small (5/32"), and the bit can wander quite a bit if the bit flexes or the blank tends to shift. I've had very good success drilling on the lathe holding the blank in standard jaws in a scroll chuck. But I will admit that I spend more time drilling the hole than I do turning the pen body! Doing very precise work can be satisfying.