What are the names of the feuding families in "The Interlopers"?

The two feuding families involved in a fierce land dispute are the Gradwitz family and Znaeym family. Both families are feuding over a narrow, precipitous strip of woodland, which is not considered valuable or sought after property. Many years ago, Ulrich von Gradwitz's grandfather had won a lawsuit against the Znaeym family, which declared the narrow strip of woodland his legal property. However, the Znaeym family refused to acknowledge or honor the court's decision and continued to poach on the land. Both Ulrich von Gradwitz and Georg Znaeym inherited their ancestors' feud and deeply detest each other. At the beginning of the story, Ulrich von Gradwitz and his men patrol the territory in hopes of finding someone from the Znaeym family to kill. The two enemies end up discovering each other in the forest but a strong storm knocks down a massive tree, which incapacitates both men before they can harm each other.

How did the feud between the two families in "The Interlopers" start and why does it continue?

Ulrich's grandfather sued George's ancestors because they had illegally possessed a strip of land on Ulrich's grandfather's property. Ulrich's grandfather won the lawsuit, meaning George's ancestors should have given up the land. However, despite the ruling of the court, George's family continued to poach on this strip and "similar scandals had embittered the relationships between the families for three generations." So, each successive generation of the two families continued to feud with each other. The feud had become a tradition or a habit. 

Ulrich becomes the head of the family and takes the feud more personally. George also "inherits" this feud and, for his part, continues to poach on the strip of land. "The feud might, perhaps, have died down or been compromised if the personal ill will of the two men had not stood in the way . . . " Like the generation before them, George and Ulrich inherited an argument that was initiated by their ancestors. The only way to stop the feud is to take personal feelings out of it and to realize the futility of sustaining an argument over a piece of land that was "not remarkable for the game it harbored or the shooting it afforded." 

What has kept the feud between the families going for three generations in the short story "The Interlopers"?

This is a good question. Since the text does not say explicitly why the feud lasted for so long, we need to infer the reason for the long feud. Based on the text, we can say that there are two reasons for the feud. 

First, the land has always been in dispute. According to the text, the courts finally decided in favor of the family of Ulrich von Gradwitz, but the family of Georg Znaeym did not accept it as a just ruling. Therefore, this dispute continued.  At this point it is more an issue of personal pride, because the land is not a particularly good tract of land. The text is clear about this point. Hence, the pride of the men stand out. Here is a quote on this point:

The neighbor feud had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to, it was Georg Znaeym, the inheritor of the quarrel and the tireless game snatcher and raider of the disputed border forest.

Second, there is evidence that the two men did not get to know each other. Once the rift took place, there has been little cordial or constructive contact. Within this context, the two men just hated each other more and more. This makes sense, because it is easy to demonize imaginary people. That we are on the right track is confirmed. When the men come face to face under a fallen tree, they quickly reconcile. 

What has prevented the feud from ending in "The Interlopers"?

Rigid family honor and landownership have prevented the feud from ending in Saki’s short story “The Interlopers.” Two families—Gradwitz and Znaeym—harbor a longtime dispute over a small parcel of land, a “narrow strip of precipitous woodland” lying between the Gradwitz family’s woodland and the Znaeym family’s plot. The most recent descendants of each families are Ulrich von Gradwitz and Georg Znaeym.

Decades earlier, Ulrich’s grandfather won a lawsuit that seized this narrow strip of land

from the illegal possession of a neighboring family of petty landowners; the dispossessed party had never acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations.

When the story opens, Ulrich patrols his forest land for Georg. Raised with and having inherited this feud and rancor toward the other family, both men perpetuate this feud that

had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to it was Georg Znaeym, the inheritor of the quarrel and the tireless game-snatcher and raider of the disputed border-forest.

The two men do not even know each other but automatically assume animosity toward each other based on family pride and a sense that the other person is an “interloper” or intruder upon the disputed land. The land feud, which has devolved into a battle of hatred, perhaps would have

died down or been compromised if the personal ill-will of the two men had not stood in the way; as boys they had thirsted for one another’s blood, as men each prayed that misfortune might fall on the other.

Ironically, both men are interlopers in that forest land; only nature can end the feud. When Ulrich and Georg meet face to face and before either can draw a weapon, a tree crashes down on them. Injured and pinned under branches, neither man can challenge his enemy or even leave the scene. After cursing each other and claiming that their respective parties will show up, they eventually realize that no one is coming to rescue them.

Ulrich finally offers Georg a drink, which Georg initially spurns. Seeing Georg in pain and exhaustion (and feeling the same way himself), Ulrich senses “the old fierce hatred … dying down” in himself. He extends an olive branch:

We have quarreled like devils all our lives over this stupid strip of forest, where the trees can’t even stand upright in a breath of wind. Lying here tonight thinking I’ve come to think we’ve been rather fools; there are better things in life than getting the better of a boundary dispute. Neighbor, if you will help me to bury the old quarrel I—I will ask you to be my friend.”

After a stretch of silent thought, Georg accepts Ulrich’s friendship and admits

what peace there would be among the forester folk if we [the two families] ended our feud to-night. … I never thought to have wanted to do other than hate you all my life, but I think I have changed my mind about things too, this last half-hour. And you offered me your wine flask. ... Ulrich von Gradwitz, I will be your friend.”