Map what’s on the ground: if it’s using Traditional Chinese, then use Traditional Chinese. But there’s a way to include Simplified Chinese - try asking Singapore / Hong Kong / Taiwan OSMers around to ask for input on how to do that. Perhaps ask in OSM Help Forum - no problem directly asking in Chinese, because you might get direct answers easily.
Let me know about this, because I could update the (Malaysian) OSM Wiki regarding this matter.
Click here to enlarge - The street in question
This is in Traditional Chinese, right? So, without doubt, name:zh should be in Traditional Chinese. Also, from what I observe (areas around Kedah), old shops tend to use Traditional Chinese. But new ones might switch to Simplified.
Well, I leave the rest to you guys whether to stick with Simplified or Traditional for other places without a visible name sign.
Disclaimer: I cannot read Chinese at all, but using Google Translate and/or this tool, at least I could have a go to input name:zh values. 
Incorrect name values could probably coming from me. And I’m aware that the standard Mandarin language syllabus in Malaysia is using Simplified. Welp, that’s so complicated.