Learn Hardcore Chinese: wǒ hái xiǎng tīng nǐ shuō nǐ de míngzi.

If you’ve already asked something else and want one more thing, 还 = “also/in addition”: “I also want to hear you say your name.”
If you expected to hear it but haven’t yet, 还 = “still”: “I still want to hear you say your name.” Tip: when 还 is used with negatives (e.g., 还没), it usually means “still/yet”: 我还没听到你的名字。

Why is 你 repeated (in 听你说你的名字)?

Because the first 你 is the subject of 说 (“you say”), and the second 你 is the possessor in 你的名字 (“your name”). Chinese normally marks possession with 的. If you drop the second 你, 听你说名字 sounds odd/ambiguous (“listen to you talk about names”). To avoid repetition, you can rephrase:

我还想听你说你叫什么名字。
请告诉我你的名字。

Is 说你的名字 idiomatic? Should I use 告诉 instead?

说你的名字 is fine when you literally want the person to say their name out loud (e.g., mic check, roll call). For general “tell me your name,” 告诉 sounds more natural/polite:

请告诉我你的名字。
我想知道你的名字。 If you want “say it out loud,” add a result complement:
请把你的名字说出来。

Why use 听 and not 听到/听见?

听 = to listen (the activity/intention): 我想听你说… “I’d like to listen to you say…”
听到/听见 = to hear (the outcome): 我想听到你说… emphasizes actually hearing it; 终于听见你的名字 “finally heard your name.” Use 听 to focus on the act; use 听到/听见 to emphasize the result.

What’s the nuance of 想 vs 要 here?

想 = “would like to,” softer and polite: 我还想听…
要 = “want to / going to,” stronger/insistent: 我还要听… can sound demanding or like a decision. For requests, 想 is safer.

How does the structure 听你说你的名字 work?

It’s a verb taking a clausal object: 听 [你说你的名字] = “listen to [you say your name].” This pattern is common:

听他讲故事 “listen to him tell a story”
看她做菜 “watch her cook”

Can I make it more polite by using 您?

Yes. Replace both occurrences:

我还想听您说您的名字。 Even more natural/polite when asking a stranger:
请问，怎么称呼您？

What’s the most natural way to ask someone’s name?

Common options:

你叫什么名字？ neutral/informal
你叫什么？ very casual
您贵姓？ polite; asks only for the surname
怎么称呼您？ very polite; “How should I address you?”
If you just want the info: 我想知道你的名字。

What does 的 do in 你的名字? Can I drop it?

的 marks possession. You generally cannot drop it here; 你名字 sounds off. Omission is common only with close relationships/titles (e.g., 你妈、你哥、你老师), but not with 名字.

说, 讲, and 告诉 — which one fits?

说: general “say/speak.” OK with 名字: 说你的名字.
讲: “talk about/explain/tell (a story).” Often used in Taiwan for “speak (a language).” Not natural with 名字: avoid 讲你的名字.
告诉: “tell (someone) [information].” Needs an indirect object: 告诉我你的名字 is very natural.

Any pronunciation tips (tones, neutrals, sandhi)?

名字 = míngzi (second tone + neutral tone).
的 = de (neutral tone).
还 = hái (second tone).
我还想: the 我 (wǒ) is a third tone pronounced as a low 3rd before a non-3rd tone; you don’t change the written tone, just pronounce it lightly.
说 = shuō (first tone), 听 = tīng (first tone), 你 = nǐ (third tone).

Does 我还想听你的名字 mean the same thing?

Not exactly. 听你的名字 = “hear your name (mentioned)” without specifying who says it. If you want the person themselves to speak it, keep 听你说你的名字 or use 请告诉我你的名字 / 请把你的名字说出来.

If I mean “again/one more time,” should I use 还 or 再/又?

Use:

再 for “again (in the future/planned)”: 我想再听你说一遍你的名字。
又 for “again (already happened)”: 他又说了一遍他的名字。 还 by itself doesn’t mean “again,” though 还想/还要 can imply “in addition/another.”

How can I soften the request?

Add softeners:

Reduplications/briefness: 说一下 / 说说 / 说一遍
Polite frame: 可以吗 / 好吗 Example: 我还想听你说一下你的名字，可以吗？

What would this look like in Traditional characters?

我還想聽你說你的名字。

Does 听你说 ever mean “I heard you say…”?

Yes. As a set phrase, 听你说，… means “from what you say / I hear you (said)…”

听你说，你最近很忙。
For “I heard you say your name (before),” use 过: 我听你说过你的名字。 In your sentence, 想 makes it a desire: “I (still/also) want to listen to you say your name.”