当然可以。如：

He was well-known for his violent and threatening behaviour. 他因暴力和威胁行为而有恶名声。《简明英汉词典》

Her cupidity is well known. 她的贪婪尽人皆知。《简明英汉词典》

请问 be well-known 可否表示臭名远扬这类的闻名吗？还是另有新词表达？谢谢了！

回答如下：

well-known 修饰人是，通常表示好胡方面，也可以标上坏的方面，还可以表示，事物

He is well-known for robbering others of money.

他以抢劫他人财物臭名远扬。

She was well-known two years ago.   
两年前她就出名了。

The writer is well-known for being productivity in works.   

该作家因其多产而闻名。

He is little known as an artist.

他是个不出名的艺术家。

Our silks are known for good quality.

我们的丝绸是以质量出名的。

His championship of women's rights is well known.

他提倡女权是众所周知的。

Auroras are known to have many shapes and colors.

众所周知的是极光有许多形状和颜色。

The well-known singer was accompanied at the piano by my sister.   
我妹妹为这位著名歌手担任钢琴伴奏。

Two well-known firms of drug manufactures are cooperating and attempting to find a cure for cancer.   
有两家著名的制药厂正在合作试图找到一种治疗癌症的药物。

be well-known  adj.尽人皆知；见称于世

To get quality cores, core shooting process must be well known.  

为了获得优质的砂芯,必须对射砂过程有充分的了解.

We're sure you'll be well - known as an artist.  

我们相信你会成为一位著名的画家.

 It may be a well-known fact, but I didn't know it.  

这可能是人所共知的事实，但我却不知道。