Beyond both Victor and Tony being uber-geniuses who invented and wear incredibly powerful armour, there's not much direct connection. In fact, Doom invented his mask and suit while studying in a hidden monastry with Tibetan Monks. And since Dr Doom debuted a few months before Iron Man, it means he was actually the first to build Powered Armour,
"In a cave! From a box of scraps!"
Victor did try to redeem himself by taking Tony Stark's place and becoming the Infamous Iron Man at one point.
Amusingly, Doom is possibly the only Marvel character even more arrogant than Tony Stark, although given his incredible skills, powers and victories, his massive ego is somewhat justified. Tony can at least match Doom in Robotics and associated fields, but he has next to no knowledge of Magic, while Doom is second only to Dr Strange in that field.
And while Tony is a decent fighter at best without his Suit, Doom is a Master of the Martial Arts. At one point a ridiculously powerful enemy strips Doom naked and transports him millions of years into the past. Doom is attacked by a Prehistoric, "Lion". Victor kills it with a single punch from his bare hand. Then eats it, and uses the hide, bones etc to make a primitive version of his mask and armour.
Doom is what you get when you take Batman With Prep Time as your baseline for a character. And then Turn the Knobs up to 11.