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In my book, $n(\ce{Na2CO3})$ was used to indicate the number of moles of $\ce{Na2CO3}$ without any clarification. Is it common knowledge among chemists that $n(\ce{Na2CO3})$ indicates the number of moles of $\ce{Na2CO3}$?

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Yes, the standardized quantity symbol according to ISO 80000-9:2009 Quantities and units — Part 9: Physical chemistry and molecular physics as well as the recommended quantity symbol according to IUPAC Quantities, Units and Symbols in Physical Chemistry (Green Book) for amount of substance is $n$.

The quantity “amount of substance” shall not be called “number of moles”, just as the quantity “mass” shall not be called “number of kilograms”. In the name “amount of substance”, the words “of substance” can for simplicity be replaced by words to specify the substance concerned in any particular application, so that one may, for example, talk of “amount of hydrogen chloride”, or “amount of benzene”. Although the word “amount” has a more general dictionary definition, this abbreviation of the full name “amount of substance” may be used for brevity.

Thus, $n(\ce{Na2CO3})$ would be called amount of sodium carbonate.

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You are unclear if you are confused by $n$ itself, or by the particular notation $n(\ce{Na2CO3})$

$n$ is widely accepted to denote amount of substance, expressed in moles, as @Loong , IUPAC and Wikipedia say.

If $n$ means the amount of the particular substance like $\ce{He}$ or $\ce{H2O}$, it is often written in index form like $n_{\ce{He}}$ or $n_{\ce{H2O}}$.

Multiple levels of sub/superscripts often bring typographic difficulties. For these reasons, instead of typing $n_{\ce{Na2CO3}}$, some may prefer rather $n(\ce{Na2CO3})$ instead.

It is not official recommendation and less controversial may be substitution by some placeholder.

I often think the term amount of substance has been chosen rather unluckily, as at overlap with less scientific domains, the term can be confused with primary understanding of amount in common language with very vaque meaning.

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  • $\begingroup$ Who recommends writing amount of sodium carbonate as $n({\ce{Na2CO3}})$? Is it IUPAC? I don't recall seeing this recommendation in textbooks? $\endgroup$
    – ACR
    Commented Dec 27, 2021 at 0:43
  • $\begingroup$ It is not official recommendation, rather practical one, applicable generally on complex indexes, not just on amount of substance. I remember one of mods suggested it. $\endgroup$
    – Poutnik
    Commented Dec 27, 2021 at 6:07
  • $\begingroup$ This is I am wondering, who is making this practical recommendation? $\endgroup$
    – ACR
    Commented Dec 27, 2021 at 6:10
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    $\begingroup$ Personally, I think less controversial way would be substitution method, like let A is <complex formula>, then using $X_\mathrm{A}$, where X is general quantity. As $n_{\ce{^{235}_{92}U}}$ or similar may not always look good. $\endgroup$
    – Poutnik
    Commented Dec 27, 2021 at 6:25
  • $\begingroup$ Yes, I have seen subscripted versions but rarely with in-line brackets. $\endgroup$
    – ACR
    Commented Dec 27, 2021 at 6:30