If your world does not have family names, if people of the same name1 are distinguished from each other by bynames as well as nicknames --
Don't make them all the same pattern.
The one I see most often is that they are, every man Jack and every maid Jill, called Name the Adjective. All of them. Robert the Wise. John the Loyal. Joan the Prudent. Richard The Lionhearted.
At the very least, some would be merely Name Adjective (or Descriptive Noun): Jack Lean. Joan Tall. Sally Haltfoot. Will Scarlet. Robin Hood. John Sheepshanks. John Lackland.
At that, some would be Adjective Name: Little John, Fat David, Red Robert. (Fun fact: Little John's name, while ironic, may have meant nothing more than John, Jr. in the usage of the day when the ballads were sung.)
More likely they would be varied.
Some would be locatives: John of the Woods, Jack under the Mountain, Sally Meadows.
Note that the larger the location they are named after, the farther off they acquired the byname, and likely, the farther off they still are.
The Robin Hood ballads have two characters known by locatives, David of Doncaster, a Merry Man, and Roger of Doncaster, the villain in Robin Hood's death. The oldest Robin Hood ballads often put Robin and his band in Barnsdale Forest rather than Sherwood, and Doncaster is a town near that forest -- yet, not so near that it actually appears in the ballads.
Then there's Marie de France, a famous medieval writer, who worked in England, not France.
Some would be occupational references: Alice Webster, Wilma Alewife, John Smith, John Black (short for Blacksmith), John Coward (or Cowherd).
Note how at the time when bynames calcified into surnames, there were a lot more farmers than smiths. Yet Smith is far more common than Farmer as a surname, because it was far more likely to be unique in combination with the personal name. Bynames have to indicate which person is meant. (Given the lesser amount of travel, quite a few bynames indicate which person among a group of people you are already knowledgeable about.)
Some would be patronymics -- Roberta Robin's daughter -- or matronymics, even in a patrilineal society, if the father is unknown, if the mother is widowed or has the more forceful personality so she's the one people think of, or if the mother just has the more distinctive name -- Robert Maud's son, instead of Robert Robert's son, where people would have to ask which Robert Robert's son.
Some will combine patronymics with the occupation: John Masterson, Will Millerson, Tom Smithson.
Some would be even more odd. Isabelle Romée, mother of Joan of Arc, has a byname that indicates a pilgrimage to Rome. The byname Duckerell means "little duck" but why it was applied to a man is unknown.
While Robin Hood's byname is perfectly commonplace for a man noted for either making or wearing a hood, there are also records of his full name being used as a single-word last name: John Robinhood, Will Robinhood, David Robinhood, Eleanor Robinhood. This very unusual structure is used mostly (though not exclusively) for criminals, thus confusing issues about the sources for the legend. (There is, in fact a deep debate about one passage, where a man might be referred as "Robinhood" only after being outlawed, but the writing is so crabbed that he might still be called "Robbeson.")
At that, when using the adjectives, they tend to go for the obvious (at least to those familiar to him), not the flattering. Calling a man "John the Loyal" is unlikely; "John the Lean" is more likely, though it may be ironic. "The Loyal" would be for a man known for some deed of loyalty, or else for someone you wished to flatter.
More, they were less hypersensitive to slights. As witness that in the 20th century, a sociologist could not explain to one Chinese informant why he thought the man might object to his being known as "the stutterer." The stutterer was flabbergasted at the very notion. He stuttered. Why wouldn't they identify him so?
Also, they change. Sometimes. There's a historical character who in his own time was known as "William the Bastard" and "William the Fat" as well as the one that is generally used in histories: "William the Conqueror." (It was the middle one. "Bastard" was youthful, and "Fat" was old age.)
On the other hand, sometimes they stick. Little John, I mentioned, was a form of John, Jr, but it was perfectly normal to go with it after Big John was shorter than his son. Alys Webster might have worked at weaving for a few years before marrying and giving it up, but since they were used to calling her Webster, they might have just gone on calling her that. John Lean might have turned into the stoutest man in the village after his lean youth.
It's probably wiser for a writer to use one that stick when it's no longer right than for it to change, if only to avoid confusing the readers, unless the name change is part of the story. Such are the adventures of bynames.
There's a meme floating around right now (did I see it in one of Sarah's collections?) of a picture of someone's cell phone contact list with names like "John the plumber" and "Neighbor Jane" and things like that with a caption expressing understanding of how family names came to be.