So first, I'd take issue with the premise that place names are unimaginative in East Asia (going a little broader than just the PRC for this one).

The ya and lu in yalu mean duck and green respectively.

They don't, though. The characters used to transcribe the likely-Manchu name have those readings, but that's not what it actually means. Don't confuse characters for etymologies. A huge number of place names in China (and Taiwan and the surrounding areas) aren't actually originally Chinese.

I've been living in "new bamboo" in Taiwan. This is a renaming of the old town "bamboo fortress" (zhu qian), however the city wasn't actually called "bamboo fortress". If you say "bamboo fortress" in Taiwanese, it's "tekcham", which sounds kinda like what the Taokas aborigines called their own settlement. That did their name mean? No idea, but you can be darn certain it wasn't "bamboo fortress", just as neighbouring "Seedling Chestnut" is a Mandarin re-writing of the Hakka "Cat - Racoon dog", which wasn't the original name either, since it too was an aboriginal name, pronounced /βari/ in Matu'uwal which is spoken there now, though the Taokas pronunciation was probably also slightly different.

"Taiwan" is also not originally a Chinese name. Really even just sticking to Taiwan the examples are endless. Mainland China is no different. Any place name in Inner Mongolia that includes 部落 buluo isn't going to have been Chinese.

Chances are, if a name seems odd or nonsensical to you in Mandarin, it generally means it's not originally a Mandarin name. There's a huge amount of work that's been done and is continuing to be done just on the topic of toponyms as a means of working out human migration patterns and the historical spread of civilisations.

Even the names that seem more obvious in Mandarin aren't always what they seem. For example Changzhou 常州 in Jiangsu is not "ordinary prefecture". The Chang here is with a more classical meaning of "eternal". It's quite poetic, I think. Dunhuang 敦煌 in Gansu is named for the fires that were lit to alert people to invaders. Another really descriptive and name evoking the imagery of what was significant at the time it was named.

For what it's worth, Shanghai doesn't actually mean "on the sea" like people tend to think today. There was a historical Xiahai nearby. The original meaning wasn't any more amazing. I just bring it up to point out that the modern names don't always mean what people think they mean, much like your Duck Green River example. And even earlier Shanghai was called Hudu, named for the bamboo fishing weirs commonly used in the region. It was a name that was incredibly characteristic of the economy and environment of the time and place.

Do western cultures have the same issue, but it's just obscured because they're in archaic forms of the language?

You mean like the great state of Green Mountain or the state named after the red coloured river? Western cultures have it, but just like a Chinese person doesn't think about Beijing meaning "northern capital", American's don't really spent a lot of time thinking about how "nevada" means "snowy", because it doesn't; it just means "Nevada". /u/124876720 has covered this topic well already.

Just remember that when you say Mississippi ("big river") or Australia ("southern place") you're not actually going through the etymology each time you say it. You're just saying the specific sounds that refer to the place you're talking about.

I can't answer your questions directly, but wonder about your premise. If Chinese place names are more likely to be straightforward descriptors, that would be an interesting fact and I'd also like to know why. But perhaps the "utilitarian" names just stand out more to you, and seem more common for that reason (availability bias?).

For example, lots of others aren't: Bohai Sea, Yalu River, Hangzhou, Shaanxi, Taishan, Yantai, Shenzhen, Chongqing... and many, many others.

Can you give examples of non-Chinese names that are, in your opinion, "more imaginative" than those of China?

Do western cultures have the same issue, but it's just obscured because they're in archaic forms of the language?

Mostly this. Lots of places in Western Europe and the United States have fairly straightforward meanings, but multiple waves of demographic and linguistic shifts have rendered the original semantics opaque to the peoples who inhabit those places today.

A few examples in the United States:

Pennsylvania == Penn's Wood's
Vermont == Green Mountain
Palo Alto == High Wood
Mississippi == Big Water, in whatever Indian language

From Great Britain:

Colchester == Colne Caster == Colonial Fortress/Camp
Cambridgeshine == Shire (county sea) of Cambridge. "Cambridge" is actually derived via sound-changes from the Old English Grantanbrycg which means "Bridge on the River Granta". The Granta is a tributary of the modern Cam, which apparently changed names with it's tributaries at some point in the past, possibly due to changes in the course of the rivers over time.

I'm hardly an expert on place names, but these are few I was able to quickly look up from reliable sources (mostly the O.E.D.).

Many towns and cities in North America are either derived from mutated versions of geographic names in various Native Indian languages (ex: Chicago, Miami, Sandusky, etc), or named after places in the Old World such that they lost any etmoloygical connection to their original meaning (New York, Worcester, Denver).