What's the name and purpose of the large prominent vein on the top of my penis that seems to originate from the pelvis?

Here are some...: Most likely, what you see are dorsal veins. Known to us, veins of any organs tend to widely vary in number, course, and distribution as compared to the arteries to any organs. So, if asymptomatic, compressible, and variable at erection and detumescence, leave them alone because what you see is your personal unique anatomical variation. Of course, if still in doubt, have someone take a look. Best..