Does baking time increase when making multiple Pumpkin Bread Puddings?
It mostly depends on whether you're able to arrange them in the oven with plenty of space. If they all fit on one rack, with a few inches between the pans, it should be basically the same baking time. They're all still in an oven of the same temperature they'd be in if baked alone.

But if things get crowded, especially if you have to put them on the top and bottom rack, with one at least partially over another, then you may need increased baking time. They'll essentially shield each other, i.e. the air will end up a little bit cooler in the area between them. In that case you'd probably also want to rotate and shuffle them around once or twice during baking, to avoid them browning more on the exposed parts and less on the shielded parts.



The oven will also take slightly longer to come back up to temperature with more in it, but likely on the scale of a difference of a minute or two as long as it's a completely preheated full-size oven, so for something that's baked 30-40 minutes you don't really need to worry about. The most direct information I found about this was from BakeWise: 


  Even if you have a well-preheated oven, if you open the oven door ... (the time that the oven was open can be over 1 minute) the drop in the oven temperature can be 175F/79C). Recovery time can be several minutes.


So having more bread puddings does extend that recovery time, not just by putting cold mass in the oven, but also by requiring the door to be open longer while you're loading them into the oven. But again in this case that's not the important factor; even if it adds a couple minutes to the baking time, you still need to worry more about the air circulation, and you were already checking in a 10 minute range anyway.