What are proper names?

I reviewed the past posts regarding this subject and found to be inadequate, partially possibly due to my fault. Aside from that, can you help me to understand better?

Do we always capitalize the proper nouns?
Proper names (often called proper nouns), are the names of specific, unique entities. Proper nouns can easily be distinguished from common nouns in English because proper nouns are indeed always capitalized. There's not much more that can be said on the subject, so I'll resort to examples:

-The man ate a big piece of pizza.

-Bob Johnson ate a big piece of pizza.

Here one can see the difference between a proper and common noun. Both sentences refer to the same subject performing the same action. After reading the first sentence, we know that a man is responsible for eating the pizza, but the common noun "man" doesn't offer us any insight (beyond gender) as to whom that person may be. In the second sentence, the use of a proper noun makes it clear that the man is "Bob Johnson".

-A rolling stone gathers no moss.

-Mick Jagger is a Rolling Stone.

The first sentence here has no proper nouns, and the second has two. The important question however, is why "rolling stone" is a common noun in the first sentence, but a proper noun in the second. The answer is that "rolling stone" in the first sentence refers to just that: a stone, any stone, which rolls. A "Rolling Stone" in the second sentence is a member of a specific band called The Rolling Stones.
Thank you very much.

Why did you place "a" in front of "Rolling Stone" eventhough Stone it is articling for is in parentheses like here?

A "Rolling Stone" in the second sentence is a member of a specific band called The Rolling Stones.

Also, is the proper name here is "The Rolling Stone" or "Rolling Stone"?

Sorry for sounding too picky but will appreciate your help.
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"The Rolling Stones" is the name of the band, thus;

Mick Jagger is a member of The Rolling Stones.


Mick Jagger is a Rolling Stone.

Another example would be;

George W. Bush is a member of the Bush family.

The President of the United States is a Bush.

Here's another;

Bart is one of the Simpsons.

Bart is a Simpson.

And another;

He is one of the teachers.

He is a teacher.

I don't know how to describe the usage of 'the'. The rules are built into my brain but I cannot describe it because it's a natural thing. The 'a', 'an', 'the' or nothing rule can be tricky, but 'a', 'an' or 'the' can never be next to each other. You can never say 'A The Rolling Stones', because, well, I don't know. It just doesn't make sense. But in this case you're talking about ONE Rolling Stone, so you must use 'a'. Because you use 'a', you can't use 'the. So it becomes 'a Rolling Stone'. And of course it cannot be 'a Rolling Stones'. Hope that makes sense.
Xess gave some good examples, and I'll add what I can. "The Rolling Stones" is the full name of the band in question. If the word 'the' were not part of the band's name, then it would not be capitalized, and you would see it would see it written as "the Rolling Stones". The word 'the' is a definite article, which means that it precedes a specific singular or plural noun that's part of a larger group . So even if 'the' were not part of the band's name, we know it would be the article used, because we are referring to one specific band (bands being the larger group or category) which goes by that name. In contrast are the indefinite articles 'a' and 'an'. Indefinite articles are used before any non-specific singular nouns which are part of a larger group. Because Mick Jagger is only one of many Rolling Stones, we must use an indefinite article to describe his status. Writing that "Mick Jagger is the Rolling Stone" makes it sound as if he is one single person known as "the Rolling Stone", which is not the case.
although i tend to type without any capitalized letters (force of habit), i'll attempt a simple explanation.

you can think of proper names as proper nouns. a proper noun is a name of a person, a place or a thing. for example:

Arvin Emotion: it wasnt me or Mr. Gatmaitan = name of a person

Earth, America, New Jersey, East Brunswick, Parsons road (where i'm from) = names of places

Microsoft, Wall Street Journal, Bose (software, newspaper, electronic equipment) = names of things

the first letter of proper nouns must be in UPPER CASE - as seen above and below.

Arvin is from New Jersey. Arvin does not own Microsoft. and so on.

a proper noun must start with a capital letter, regardless of where you use it in a sentence.

hope that helps.
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By following your reasoning, is it the case that if a band named "Smelly Rose" is playing in a house, we can say like the sentence below?

Welcome all. As advertised on newspapers, the Smelly Rose is playing in the house. Enjoy the performance. (the word "the" is not capitalized.)

As a reminder, you said in the post that even if "the" were not part of the band's name, we know it would be the article used, because wer are referring to one specific band which goes by that name. and bands being the larger group or category.
I had a band before named "Imago". But I am now part of a band called "Eternal Now".

When people would introduce Imago right before we play, they would sometimes say, "...and now, please welcome the Imago band!"

I hated that. The proper introduction is, "...and now, please welcome Imago!"

So similarly, in the case of Smelly Rose, they should be introduced as, "...and now, please welcome Smelly Rose!"

My name is Arvin. And if someone were to introduce me, they should not say, "... and now, please welcome the Arvin!", right? They should just say, "... and now, please welcome Arvin!"

In reference to your advertisement, it should read:

Welcome all! As advertised in the newspapers, Smelly Rose will be playing tonight. Enjoy the performance!

Hope that helps,