Yeah no, Psychopath's wouldn't think they are evil. In fact, the very concept would be utterly alien to them because they could not comprehend nor feel the pain they inflict on others. No empathy. No capacity for love and affection. They wouldn't be capable of caring about whether they had a girlfriend/boyfriend/husband/wife or anything like that, because it wouldn't matter to them either way.
A sociopath is capable of feeling all the range of emotions regular humans do, except they tend to express those feelings in twisted ways. Very aggressive. Very low emotional-intelligence. Yet, they can and are capable of love and empathy, it's just not expressed in the most healthy of ways. Hell, a really good anime example is MOST Yandere's. They can feel extreme and twisted love, and act accordingly. A psychopath wouldn't be able to form that kind of attached obsessive love for someone.
The main difference between a sociopath and a psychopath is quite literally, whether they can empathize with their victims. Psychopath's can't. They cannot understand how another feels, and even if they could in a logical sense, it still wouldn't mean anything to them. Sociopath's are still capable of empathy. Whether they act on it, is neither here nor there. Some sociopath's are worse than others. While ALL psychopaths are potentially devastating to be acquainted with.
Still, there are cases of Psychopaths living relatively normal lives. They acknowledge that they are "different", and while it doesn't matter to them, and they feel next to nothing for anyone around them, they adapt themselves to their environments and act according to what they see around them. Plenty of them have lived their lives without anybody knowing they were psychopathic. I've actually known one. He simply said he learned by mimicking others.
He learned how and when to laugh, appear sad, when to act concerned, when to seem angry or protective, and who to express these reactions towards and whom not to. His main reasoning for doing this, was that he disliked the idea of prison and had no wish to be "cooped up in a box" as he called it. Nothing kept him from causing mayhem other than his own personal comfort being potentially violated. Psychopaths exist in broad daylight and never commit any crimes. Hell, you might even know one and not even realize they are what they are because like the guy I knew, they learned to mimic all of the right facial and emotional responses by observing others.
Another thing, while we all know of the most horrific examples of psychopath's being serial killers, these are the most extreme examples. Most psychopaths have VERY good control over themselves. Sociopaths are the ones who are impulsive and often react outrageously and crazy in broad day and have little self control.
Believe it or not, despite psychopath's being potentially far more dangerous in the most extreme of cases, you are more likely to be harmed in life by a sociopath rather than a psychopath.