Answer: Spelling Out a Drawl
riverfox wants to know "Is there a rule/permission that allows for the literal drawl of words? ('Jaaaaaaaaack!' versus 'Jack,' Daniel drawled)."
The only answer that's been discovered is "Not exactly."
This question was a real head-scratcher. None of the style guides or writing sites that were consulted even mentioned this kind of creative spelling. However, the guidance offered for two similar types of writing techniques might shed some light on this murky subject.
Eye Dialect
Eye dialect refers to altering spelling to show the reader exactly how a character (or the narrator) is pronouncing things:
"Why, Master Sanzo, Ah could almost b'lieve you're not in'erested in our charmin' company!" exclaimed Hazel, looking hurt.
Hazel's dialect in Tokyopop's translation of Saiyuki is clearly meant to be Southern U.S. One of the conventional ways of representing the pronunciation of the first person singular pronoun I in this dialect is the spelling shown: Ah. The example uses apostrophes to stand in for missing or altered sounds, such as the change of the -ing at the end of charming to an -in sound.
Some famous and beloved works have used eye dialect, including many of Mark Twain's novels and stories. However, this isn't an easy technique to do well unless you've got a very good ear for the dialect you're attempting to present and the skill to represent the sounds consistently. You don't want your reader to stop paying attention to the plot of your story while she puzzles out which word your character is trying to say.
Experts advocate giving the impression of an accent primarily by word choice and sentence structure, with only small amounts of spelling variation:
"Why, Master Sanzo, I do believe you're not interested in our charmin' company!" exclaimed Hazel, looking hurt.
Here, the phrase I do believe - often heard in examples of U.S. Southern speech - and the single easily understood unconventional spelling charmin' carry the impression of Hazel's accent without making the reader stumble every few words.
Onomatopoeia
Onomatopoeia are words that represent nonverbal sounds. Many of these are accepted dictionary words, such as gurgle, thump, or whisper, but the term also covers any made-up words ("neologisms") that the author might want to create. The term includes widely accepted representations of human nonverbal utterances, such as hmm for the humming sound that people are assumed to make (in English, anyway) while they're thinking.
Except in casual and humorous writing (or creative writing by very young authors), onomatopoeic neologisms are difficult to use. Readers don't always react to them in the way that their creators intend. In many cases, in fact, the reader will come to a stop while she tries to figure out what's actually meant:
"Stupid monkey! Slow down before you choke!" hissed Sanzo.
Goku didn't seem to notice. He kept on kaswalloping dumplings as though his life depended on it.
Chances are that no one will have any difficulty figuring out what our perpetually irritable priest sounds like as he chastises his ward, but what exactly is Goku doing with those dumplings? The word I've made up has elements of swallowing and gulping, and the context would imply that he's eating, but the neologism is still intrusive and doesn't add anything to the story.
"Stupid monkey! Slow down before you choke!" hissed Sanzo.
Goku didn't seem to notice. He kept on gulping down dumplings as though his life depended on it.
Gulp is also an example of onomatopoeia, but it's one that would be familiar to virtually every reader.
So What About Spelling Out a Drawl?
Given the discussion above, it would seem that the consensus is against changing the spelling of words to reflect the way in which they're uttered:
"Saaaaan-zoooo!" said Goku.
The priest awoke with a start. "Arrrrrgh, it's you! What's your problem, stupid monkey?"
"I'm just happy you're back!"
Here, the second drawn-out syllable is really problematic, especially with the hyphen in that location, as many readers will end up reading it as "zoo" rather than a drawn-out version of the last syllable of Sanzo's name (which is technically his title).
However, there is no set style sheet for fanfiction. And in this case, the source material - a manga - uses this type of variant spelling all the time. In comics of every kind, where there's often no narrative voice to describe how the characters are speaking, characters scream Aaaarrrrrgh! and shout Noooooo! in word balloons.
Still, you might want to curb your variant spelling to the minimum necessary to get the job done:
"Sanzooo!" said Goku.
The priest awoke with a start. "Arrrgh, you! What's your problem?"
"I'm just happy you're back!"
If your story is a relatively serious one, though, you might be better off if you use description, word choice, and other more conventional tools to make your intent clear:
"Sanzo ... " crooned Goku, happily.
The priest awoke with a start. "You! What's your problem, stupid monkey?"
"I'm just happy you're back!"
The ellipsis suggests the open-ended nature of the utterance of Sanzo's name, and the onomatopoeic word croon and the adverb happily give us the tone. Goku is boundlessly pleased to be reunited with his master: "God's in his heaven, all's right with the world." Sanzo's abrupt exclamation, expanded to include his favorite pejorative term for Goku, carries his irritation every bit as effectively as the spelled-out snarl Arrrgh would have.
With this in mind, let's return to the original example. Rather than using changes in spelling, you could apply punctuation and introduce a bit more description of exactly how Daniel is saying Jack's name:
"Jack -" said Daniel, drawing his name out into an unmistakable warning.
or
"Jack ... " Daniel drawled, transforming that simple syllable into a complete conversation.
Your choices will depend on what you (and Daniel) are trying to accomplish in the scene.
Special thanks to green-grrl for help with the Stargate SG-1 examples!