The bolt lodged into the cat's head and he ran off.
Judge Hastings said the 18-year-old handed himself into police when a flyer appeared in his letterbox about he incident.
"This indicates to me that he did not mean to hit the cat,'' Judge Hastings said.
The man attended a restorative justice meeting with Moomoo's owner and was described by police as being exemplary in completing his court-ordered tasks.
In deciding on permanent name suppression, Judge Hastings took the man's age and that he had a clean criminal record into account.
"The cat is alive. He has made peace with its owner.''
The matter had received worldwide media attention, with reports written in the New York Post and the Huffington Post, Judge Hastings said.
"The coverage was quite unprecedented.''
He was satisfied that publication of the man's name, address and occupation would result in extreme hardship and ruled on permanent name suppression.
The police prosecutor did not oppose name suppression.
The man's lawyer Colin Ross said the case had "gone viral'', which was an unexpected result of the case.
He said his client had concerns if his community learned he was the one to have shot Moomoo.
Earlier, Wellington Cats Protection League president Susan McNair said name suppression sent the wrong message about animal cruelty.
"If you can get away with it, what does that say to the next person? It's like `I can do whatever I want. I don't have to pay anything, nobody's going to know it was me'.
"People should know who he is so they can let him know how disgusted they are in him.''
After the incident, Moomoo had to have surgery at Massey University Veterinary Teaching Hospital to remove the crossbow.