• Name

Those two long feathers are called lingzi(翎子), zhiwei(雉尾), or zhijiling(雉雞翎).

• What it is made of

Let's look at the word zhiwei(雉尾). Zhi (雉) is a family of bird known as Pheasant, and zhiwei translated literally, means the tail of pheasant.

• Origin

The written record of lingzi can be traced back to as early as Han dinasty(漢朝). As written in Book of Later Han(後漢書):

武冠...，加雙鶡尾，豎左右

The crown/hat of warrior..., add a pair of pheasant tails, erected both left and right.

Later on Southern and Northen Dynasties(南北朝), written in Book of Qi(南齊書):

唯武騎虎賁服文衣，插雉尾於武冠上。

Only brave warriors may wear pheasant tails on their crown/hat.

wenyi(文衣) were nice looking clothes that were wore solely for their appearance. These records implied that in those times, only the brave warriors may put pheasant tails on their hat.

Later on, thanks to abundant of pictures (even photograph), we can find another popular usage of lingzi which we have clear pictures of: in Qing dinasty(清朝), as they were put on the hats wore along with precious stone (crystals, ruby, etc.) by goverment officials. The lower rank officials in Qing dinasty that wore hats with lingzi, had their lingzi made from 鶡(some kind of blue-brown pheasant)'s tails. The higher rank officials wore one with lingzi made from peacock tails; the more eyespots (up to three) on that tail, the higher his rank. The lowest ranks didn't have any jewelry nor linzi on their hat. But the lingzi wore by Qing goverment officials are stacked, and not erected.

The modern image of erected, really long lingzi, came from Beijing Opera(京劇), that rose its popularity in Qing dinasty. The lingzi is used to give the impression of "dashing", "handsome", and "brave warrior", usually wore by prominent characters that is good at battle such as Lu Bu(呂布) or Zhou Yu(周瑜) of Three kingdoms. To give such impression, appearance alone may not be enough, so the actor of the opera will perform dance, making the best of lingzi to impress their audience. Such dance is also known as 翎子功(I don't know how to translate this, let's just settle with "linzi dance"). Side note: Although the usage of lingzi in dancing can be traced back to Zhou Dynasty(周朝), they were not usually put on hats until Beijing Opera.

• Sources and more read (in Chinese):

中國服飾史 - The history of Chinese costume

戲曲藝術 - The art of opera

and my history teacher

Edit: I'm not really good at translations

I'm not an expert by any means, but I'd like to point out that the period you're referencing is pre-medieval. Chinese Medieval Armour was developed during the Song and Tang Dynasties, whereas Dynasty Warriors takes place several hundred years before, during the Warring States Period.

Also it may help Historians answer your question with a more realistic rendition: Replication Chinese General Yue Fing's Armour note the feather adornment is not nearly so exaggerated. Feather attachments like in the video game Dynasty Warriors would become a liability as you're giving the enemy a great opportunity to impair your vision. All one would need to do is tangle one of those long dangling feathers with their polearm and pull, and your helmet would be off-kilter, obscuring your vision.

Non Expert opinion (I'll remove once a real historian builds upon it, but IIRC this is the reason): The Feathers are markers so infantry could pick out their officers from their fellow infantry.

Edit: /u/axitanull tells that the feathers were used as displays of bravery and prestige. While my answer is similar, I struck it out because his post is much better sourced and written.

I can't answer whether that style was common for generals, but I can answer why that particular person is represented that way.

That's an image of Lü Bu, who died in 199 CE - Dynasty Warriors is set in the Three Kingdoms period, which isn't medieval. It's also based heavily off the historical fiction novel Romance of the Three Kingdoms, so don't take its representations as fact.

Representations of him wearing two long pheasant feathers are pretty common in later periods - see this Qing dynasty print that accompanied a copy of Romance of the Three Kingdoms.

This portrayal of Lü Bu goes back at least as far as the original text of Romance of the Three Kingdoms, where he's described as wearing a cap, "with long pheasant feathers protruding from each side of the cap"

However, Romance was written a thousand (!) years after the events it describes happened, so the fact that he's described that way doesn't say much about whether he, or other generals actually dressed that way.

I looked in the Records of the Three Kingdoms, a text written only a few decades after the close of the Three Kingdoms period (although about a hundred years after Lü Bu's death) chronicling the events, and which has a chapter about Lü Bu, but it doesn't mention a hat, or feathers. Romance is loosely based on Records.

Unfortunately, there doesn't seem to be an online English translation of Records, and my Classical Chinese isn't strong enough for me to feel confident providing a translation of that section.