My father's company is named the following:
Xyz Trading Co. (L.L.C.)
I find the use of periods excessive, at the abbreviation of company and the last period in the parenthesis.
Is it grammatically correct?
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It is grammatically correct, as L.L.C. is an acronym, and Co. is an abbreviation; but it is certainly not the only correct option. LLC is far more common than L.L.C. in company names, though Co is not as popular as Co.
I would therefore expect to see:
Xyz Trading Co. LLC
For examples, you can google "co llc" (google ignores caps and punctuation), and see what comes up.
Wikipedia has a discussion on the use of punctuation with acronyms and abbreviations; generally, either way is grammatically acceptable (with few exceptions), though periods are definitely not as popular.
Traditionally acronyms, or more properly initialisms, used a full stop / period after each letter to show that each letter stood for something. That convention has mostly died out save for a few publications such as The New Yorker and a few others. The BBC has even gone so far as to drop capitalisation of all but the first letter as soon as the initialism becomes an acronym (i.e. the letters are pronounced as a word rather than individual letters).
If you are familiar with American TV, think of M*A*S*H. Those were the good ol' days, when TV was actually written T.V.. Alas, the full stops / periods are on their way out, so feel free to write just LLC. No one will even notice.
A company can call itself anything it wants, within reasonable bounds that would exclude, for example, highly offensive phrasing. So it doesn't really make any difference whether the name is "grammatically correct".
Having said that, (L.L.C.) probably isn't "part of the name" as such anyway. The UK equivalent Plc (Public Limited Company) used to be Ltd, which I assume actually stood for Limited Liability Company as in OP's case. I think such additions are more akin to, say, educational or professional qualifications in brackets after a person's name.
Having said all that, I doubt many companies would add the periods as in OP's case. Perhaps it's quite a small outfit, and they wanted to call attention to the fact that it really is a proper "company", not just the trading name of a couple of guys in a partnership. I'm afraid it just looks a bit pretentious to me - but as I said, they can call it whatever they like.
Having proofread a list of company sponsors for an event, many of whose names seemed to have the same structure except for the punctuation, I will confirm that they can be arbitrary and very fussy about periods and commas.
There's nothing grammatically wrong with the surfeit of periods in the OP's question, and whether any of us like it or not, I would not normalize it to what I would prefer when editing it.
I would also dispute FumbleFingers' point that (L.L.C) isn't part of the name. It is (probably) part of the company's legally registered name.
When formally noting your company via RSVP, Return Address, Business Cards or Legal Documents and Proposals either L.L.C. or "L.L.C." will show appropriate form. But, as within the paragraphs of proposals, certain printed material and or guides and contractual evidence, simple space from business name and small llc can fit I.D.