Distinguishing lowercase proper nouns in paragraphs

Solution 1:

This is a matter of style, not grammar. To start, The Chicago Manual of Style (17th ed.) does not say to use italics with the proper names of individuals or companies (unless specifically emphasizing the name as a word or phrase, for instance).

The following is what Chicago actually says about the various points that have been discussed in comments under the question.

Chicago, 5.6, "Proper nouns":

A proper noun is always capitalized, regardless of how it is used—unless someone is purposely flouting the rules {k.d. lang}.

Chicago, 8.4, "Capitalization of personal names":

Unconventional spellings strongly preferred by the bearer of the name or pen name (e.g., bell hooks) should usually be respected in appropriate contexts (library catalogs generally capitalize all such names). E. E. Cummings can be safely capitalized; it was one of his publishers, not he himself, who lowercased his name. Most editors will draw the line at beginning a sentence with a lowercased name and choose either to rewrite or to capitalize the first letter for the occasion. When a personal name includes a lowercase particle, the particle is capitalized if it begins a sentence or a note.

And, finally, Chicago, 8.69, "Corporate names with unusual capitalization":

Corporate names that appear in all lowercase in logotype and other promotional settings can often be capitalized in the usual way. A copyright or “About Us” statement on a corporate website can be helpful in determining a usage that might be suitable for regular text. Words that would normally be lowercase in headline-style capitalization can usually be lowercased (see 8.159). Spellings that begin lowercase but include a capital letter are usually appropriate for running text, even at the beginning of a sentence, as are names with additional internal capitals (see 8.154). A preference for all uppercase should be respected. If a company appears to prefer all lowercase even in running text, an initial capital can be applied as a matter of editorial expediency.

      Intel (not intel)
      Adidas (not adidas)
      AT&T (not at&t)
      Ebrary (not ebrary)
      Parsons the New School for Design (lowercase the, contrary to corporate usage)

            but

      GlaxoSmithKline
      HarperCollins
      RAND Corporation
      eBay

Having said that, before anything else, do what the client says to do. If the client's style is to use lowercase with their company name, then do so. It serves no purpose to go against their explicit wishes. (Although it would probably be a good idea to not start a sentence using their lowercase name.)

Only if the client does not express an explicit desire for the style to be used and if you want to follow Chicago style, then capitalize the company name as you normally would any other company name in running text—despite how it's normally represented otherwise. Also, use roman text rather than italics.

But should you decide to use lowercase text anyway, then the way to make it explicit that it's a company name, rather than a normal word or phrase, is from context. Write the sentence so it's obvious that it's the name of the company being discussed.

Finally, barring any other guidance, specific situations can overcome general guidance. If you do something that results in the meaning being unclear, then break with convention and do something so that it is clear. For instance, even though you would not normally use italics, if the specific name of the company makes it impossible to rephrase the sentence in such a way that it's clear the company name is a name, rather than a normal word or phrase, then use italics anyway. Just be consistent with whatever style you choose.