the meaning of "name"

A use of "of" in Collins Dictionary:

You use of after the name of someone or something to introduce the institution or place they belong to or are connected with.

the Prince of Wales; the Finance Minister of Bangladesh; the superb rock-hewn Cave Temples of Badami

I think "Cave Temples" is the name of the limestone caves. But as for the first two examples, how can "Prince" and "Finance Minister" be names? Aren't they titles? And especially for the first example, Charles was once the Prince of Wales and Charles is a name. According to dictionary, can I say Charles of Wales?

It's a badly written definition. Writing, "after the name or title," would be clearer. "Prince" and "Finance minister" are titles. Titles are often treated as proper nouns, hence "the Finance Minister of Bangladesh" (with capital letters), and proper nouns are often names.

Although the definition is not well written, the examples make the use of "of" quite clear.