That's what someone asked me the other day. My response? Stay tuned.
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Well, it appears as if the other responses to the question you asked assume a lot. As in that you know how to express yourself. They seem to think they "get it." I don't. For example, what does this mean:
"How do I introduce a character's name meaning?"
Huh? Okay, giving you the benefit of the doubt and imbuing myself with super-human perceptive abilities, "introduce their meanings" would probably imply what? That you want to know how to do what? Introduce these characters in your story? That's what the first part of your question asks?
Unfortunately, the second half implies that you want to know something else entirely. As in how to name your characters appropriately. But, appropriately for what or whom? Do you mean to the reader? Or to the story?
Regardless, these are two entirely different concepts, you understand. One pertains to when and how you bring a character to light for the first time (which, by the way, in not answerable by anyone but yourself). The other concerns what, if any, play on words you should use to describe a "good" character, a "bad" character, a "dumb" character, a "brilliant" character, etc. (We could go on with the descriptive adjectives forever, but I think Quora has a time limit here; at least, I know I do.)
So, in effect, if you're asking how to introduce characters in your story, you shouldn't be writing the story. Get it? If you don't know when or how to bring your own characters to the reader's attention in your story, how will anyone else know, least of all the total strangers you're asking for an answer!
But, if you're asking how to introduce the "meanings" behind the characters' names (and the proper punctuation is characters' and not character's—just FYI; make a note of that for the future), I have a question for you.
I mean, are you back in the late 1700s or early 1800s when writers thought they needed to tip off the reader to a character's traits (but not too quickly or easily!) through that character's name? You know, as in Henry Fielding's The History of Tom Jones, a Foundling (Squire Allworthy, Black George Seagram)? Get real. Get with it. Get smart. You don't want to do that today, tomorrow, or ever!
While I hate to be ostensibly rude, here, if you can't punctuate your sentences properly, can't word things to be understandable, and can't figure out some things as basic as when and how to introduce your characters and whether or not to tip off their nature by your choice of names for them, should you really be writing at all? Are you really ready to do so?
Sure, everyone stumbles and falls. Everyone trips and needs a helping hand up now and again. Beginning writers start at the beginning, and it often shows. But, come on. There comes a point when writers, even beginning writers, need to take their first baby steps on their own, take their lumps, and learn from their mistakes. Especially beginning writers who can't even ask a coherent question.
Heard enough, yet? If you haven't, I could go on.
Or, maybe not. I'm tired of this one.