I've written an answer on this before in an SASQ here. To reiterate with a bit more paragraph spacing:

An emperor might be referred to by one of four names: His personal name, his reign name, his posthumous name or his temple name.

The personal name was assigned at birth – it was his family and given name. This is the name by which he would be known until his accession as emperor, whereupon the characters that form his given name became taboo and other characters would have to be used as substitutes.

The reign name was assigned upon accession, and refers not to the emperor but rather the period of his rule. As such 'The X Emperor' means the emperor who reigns during the X reign, who would have personal name W, posthumous name Y and temple name Z.

The posthumous and temple names were assigned on death and specifically refer to the emperor himself. If the normal convention is to use one of these names (this is more common for early and middle imperial dynasties), it is usually prefaced with the name of the dynasty, especially for temple names. Posthumous names varied heavily in length and there are only some dynasties where they are used to refer to emperors.

Let's take some examples:

The second Tang emperor is commonly known as Emperor Taizong of Tang or Tang Taizong (唐太宗). This is valid as his temple name was Taizong and so the name refers to himself – hence Emperor Taizong. However, as his was the Zhenguan (貞觀) reign he would also be the Zhenguan Emperor, as he was the emperor of the Zhenguan reign, and not himself named Zhenguan. His personal name of Li Shimin (李世民) applies only to those activities he conducted before accession as the son of Emperor Gaozu (the Wude Emperor).

The fourth (officially, anyway) Qing Emperor is commonly known as the Kangxi (康熙) Emperor (ruled 1661-1722). As iterated above, this is because he was the emperor of the Kangxi reign and not named Kangxi himself. We would not typically refer to him by his personal name of Aisin Gioro Xuanye (愛新覺羅玄燁) as he acceded at quite a young age. Theoretically, we could call him Emperor Ren (仁皇帝) or Emperor Qing Shengzu (清聖祖), but this convention is simply not used for Late Imperial rulers.