Why could Mr. Wright's name be considered ironic in the story "A Jury of Her Peers"?

John Wright's name is ironic in a number of ways. In fact, the use of the name "Wright", which is a homophone of "right", is used on purpose in the story "A Jury of Her Peers" to delineate exactly how "wrong" (the opposite of "right") things were in the Wright marriage. 

We first come across the ironic use of the Wright name when Mrs. Hale takes a glimpse of the residence.

[...]they had gone up a little hill and could see the Wright place now, and seeing it did not make her feel like talking. It looked very lonesome this cold March morning.

It does not sound like the "right" place to be, after all. 

The most obvious instance of Mr. Wright's name being ironic is when his name, which sounds like "Mr. Right", is juxtaposed to his description. By all means, we could be playful enough with language and say that his real name should, actually, be "Mr. Wrong". In the words of Mrs. Hale, his harshest critic: 

...I don't think a place would be any the cheerfuller for John Wright's bein' in it.

While we learn that most farm men have to make the best out of the elements to make their lives easier, we also see that the women play a very important role in the household, for that same purpose. The women mend clothing, keep the home warm, cook the meals, can foods, make preserves, and maintain the family ready for all the changes in weather. This leads us to conclude that a typical farm marriage consists on two people who strongly depend on one another. We see this dynamic in the marriage of Mr. and Mrs. Hale. 

However, even John Hale says that John Wright seems to not care much about Minnie. He even says that he did not bother to ask Minnie to try to convince her husband on getting a telephone to ease the communication in the farm. 

I said, at the same time, that I didn't know, as what his wife wanted made much difference to John

The best evidence that shows that Mr. Wright's name is ironic, is in his actual influence as a husband. Mrs. Hale says that he was "cold", even though he was not outwardly a "bad" man. However, his attitude said much more than words could. 

He didn't drink, and kept his word as well as most, I guess, and paid his debts. But he was a hard man, Mrs. Peters. Just to pass the time of day with him--." [...]"Like a raw wind that gets to the bone.

This, combined with the effects of John Wright in his wife, shows how terribly the situation must have been at this household to prompt Minnie to snap at some point in time. Minnie used to be a cheerful girl who sang in the choir and wore ribbons and flowers. She was also seemingly happy, overall. However, all of that changed after her marriage. She lived in complete isolation, and at the mercy of this "Mr. Wright". When he wrung the neck of Minnie's only loving companion, the little canary who sang to her, Minnie lost the last of her sanity and killed him. 

Therefore, the name of "Mr. Wright" is, essentially, ironic in every sense of the meaning of the adjective "right", which is its homophone.