Obviously would love it if players can pick their dynasty names as in ROTK however that doesn't seem possible.

Here's my suggestion based on area / historical peerage, I'll also give some suggestions that may make some historical sense. I'm not a trained historian so feel free to correct me. and happy to be wrong.
Obvious ones:
Liu Bei - Han
Cao Cao - Wei
Sun Quan - Wu

There was a dynasty map mod that suggested the Liu's be all Han which I agree
Liu Zhang - Han
Liu Biao - Han


For starting locations, I'll reference the maps found for Spring / Autumn and Warring States maps which was how Dynasties up to Song picked their Empire names.

Historical
Gongsun Kang - Yan, his nephew Gongsun Yuan declared himself king of Yan
-Alternatives: Liao. Or historical Korean kingdom names e.g. Balhae 渤海 or 震 Zhen (which is actually more Northeast of where he's at now).

Cao Ren - Chen 陳 - based on his historical peerage of 陳侯 Marquis of Chen and is not far from his starting loc.
-Alternatives: 鄭 Zheng and 宋 Song which are Spring Autumn nations close to his start

Zhang Liao - 盧 Lu close to his start location. His peerage was 晉陽侯 Marquis of Jinyang which is in Shanxi but that would make his Kingdom Jin 晉 which is way too closely aligned with Sima Yi.
-Alternatives: 徐 which encompasses Xiapi and Pengcheng (close to his start loc)
-Alternative: Huainan 淮南，Guangling 廣陵, wouldn't be Empire names as they are area names but I just think 淮南王 sounds cool.

Xiahou Yuan - Qin 秦 or Zhou 周 based on starting location. His peerage is Marquis of Bochang which is in Shandong so too far from his starting location.
-Alternative: Xia 夏 based on belief that they were descendant of the Xia dynasty (but who isn't?)
-Alternatives: Yong 雍，Sai 塞, Zhai 翟, which were given to the "Three Qins" (Qin generals that surrendered to Xiang Yu). Those were also minor kingdoms during Spring Autumn around the area

Han Sui and Ma Chao - Liang 涼. Same area where he is at now.
Alternative - 秦 Qin, 周 Zhou, Yong 雍，Sai 塞, Zhai 翟



Sun Ben - 楚 Chu, encompasses the area that he was at now. I don't see a peerage that points to a specific location in his wiki.
Alternative: 吳, say if he wants to challenge the legitimacy of Sun Quan
-We can also pick from a collection of the Southern Dynasty names from the period after Eastern Jin, Qi 齊 Liang 梁 and 陳 Chen, however this was also because the Southern Dynasties had some control over central plains and Shandong region.
-There are also a lot of minor Kingdoms around the Poyang lake area for alternatives. 鄂 might be one. But I think people tend to pick one of the more well known Warring state kingdoms for empire names.
-越 Yue should also be considered, though it's not close to him geographically.

Huang Zu - 隨 Sui, this was the default name I believe given by the system and it is close to his starting location. Note it is not spelt 隋 which was actually a word created during the Sui dynasty to take out the "walking" radical.
-Alternative 楚 Chu, 荊 Jing, 蔡 Cai, 繒 Zeng

Shi Xie (and family) - 越 Yue based on location, we can also be specific and say 南越 Nanyue because imo the Shi's family intention would have been to dominate one region rather then the whole of China.
Alternatives: dynasty / empire names from Vietnamese empires e.g. 萬春 Vạn Xuân 大虞 Đại Ngu. These came much later than the 3K period but would be fun to have some difference in the naming schemes.

Shamoke - Ba 巴 this is the location where he is at now. Also the Ba people are separate culture from Nanman so hopefully there can be a mod that brings more diversity.

Menghuo , Mulu - 寧 Ning (name given by Jin Dynasty officials), 滇 Dian (small kingdom during Spring Autumn)

Alternatives:
-Nanzhao 南詔，Dali 大理 but these came hundreds of years after 3 kingdoms
-Shu 蜀
-Anything but Nanman. They won't call themselves Nanman because that means Southern barbarians and why would they want to denigrate themselves and their people?

Xiongnu - Zhao 趙 based on the historical Han Zhao empire from the descendents of Liu Bao. They initially named their dynasty Han 漢.

Zangba - Qi 齊 based on starting area
Alternatives: Lu 魯

Yuan Shang - Bai 拜 or 敗 based on the fact that he'll die. Joking aside 燕 Yan would be where he's at now. But since his ambitions would be all of Northern China he would have a lot of potential names: Jin 晉，Zhao 趙，Haan (note chinese spelling!) 韓, etc...

Zhang Lu 漢寧 Hanning, the name Zhang Lu gave to Hanzhong.
Alternatives: 寧 Ning, or anything from a Taoist manual that sounds cool. The 元 明 清 Yuan Ming and Qing dynasties broke off from the traditional dynasty naming schemes and I think those were words based from Taoist books, I can be wrong though.


Maps from wikipedia
Spring Autumn
https://zh.wikipedia.org/wiki/%E6%98%A5%E7%A7%8B%E6%97%B6%E6%9C%9F#/media/File:%E6%98%A5%E7%A7%8B%E8%AF%B8%E4%BE%AF%E5%A4%A7%E5%9B%BD%E7%AE%80%E5%9B%BE.png

Warring States
https://upload.wikimedia.org/wikipedia/commons/d/d6/%E6%88%98%E5%9B%BD%E5%BD%A2%E5%8A%BF%E5%9B%BE%EF%BC%88%E5%89%8D350%E5%B9%B4%EF%BC%89%EF%BC%88%E7%AE%80%EF%BC%89.png