The question as asked looks for a fallacy, so let us clarify the question by defining. For the sake of discussion, I'd propose:
A fallacy is a persuasive, but illogical form of reasoning that leads us from a set of premises to an incorrect conclusion.
You want the fallacy where:
...a person adheres to an original idea, even after it has been proven wrong
But the choice of a person to adhere to a false conclusion (presumably because they reject your proof and reasoning) isn't a 'persuasive, illogical form of reasoning'. That is to say, there can be no fallacy to describe what you are after, because your situation as described isn't itself an argument, it is a choice. What you are interested in is how people stick to ideas even though (and let us presume when you say "proven wrong", you mean it in some very narrow and technical sense that should be obvious to all parties such as a simple deductive fallacy) it borders on baffling to continue to refuse to accept. Let's exemplify.
You argue Socrates is mortal, and your opponent, after hearing the argument "Socrates is a man, all men are mortal, therefore Socrates is mortal" looks you in the eyes and strenuously and earnestly objects. Now, the question of Socrates' mortality has for many hundreds of years been settled logically (and empirically given his untimely end). Your question is, what is the fallacy at play with your opponent? The answer isn't one of fallacy (logical) anymore, but one of cognitive bias (psychological). This phenomenon of rejecting obvious evidence and proof is fascinating, particularly in the extreme with cranks and crackpots who will spend their lifetimes arguing they've found perpetual motion machines, violations of accepted laws of physics, and insisting on bizarre forms of reality.
A classic example when a person might stick with an obviously wrong claim about evidence (from which arguments are built and affect inference) is Asch's experiment with lines which shows that people make decisions other than self-evident experience. In this class study, people will often vote to claim a line is of the wrong length to conform to social pressure.
Of course, this happens in much more subtle ways, when a person who has strong emotional ties to a subject matter, for instance, and in all other matters demonstrating profound reasonableness, parts in some small way with truth as in the related concept of cognitive distortion. Biases and distortions, unfortunately, are the rule rather than the exception, and this is idea is so powerful it won Daniel Kahneman a Nobel Prize in 2002. To cite one specific bias that predisposes a person to stick with a bad argument doesn't seem possible, as the context is highly relevant to the choice. Wikipedia maintains a list, and anyone of these biases might result in a person, in your words, to adhere "to an original idea, even after it has been proven wrong".