What are the rules surrounding a hyphen following an abbreviation?

Question

For instance, if something is owned by Apple Inc. does that make the compound phrasal adjective 'Apple Inc.-owned'? Or would I omit the period?

Answer 1

This is a question of style, and different style manuals may give different recommendations. I will be following the Chicago Manual of Style (CMOS).

If you can, rephrase

The best recommendation in any unusual case is to rephrase. In your case, you could do it along the lines suggested by either Jason Bassford or jimm101.

However, if you really can't or would prefer not to rephrase, read on.

Don't remove the period

First of all, CMOS says that abbreviations which end with a lowercase letter should contain a period after that letter (with some rare exceptions that don't apply here). Second, for Apple Inc., the period is part of the proper name, and CMOS says that respecting the form of the proper name takes precedence over whatever other rules there may be (see e.g. here). So on both counts, CMOS would frown upon removing the period after Inc.

A hyphen may follow a period

CMOS does allow for things like U.S.-oriented, as documented in this entry from their Q&A (here):

Q. I’m interested in how you would treat the following issue of double punctuation:

U.S.-oriented.

I decided to omit the hyphen, which I would have otherwise used, because I didn’t like the way it looked following an abbreviation period.

A. It may look a little odd, but the hyphen is conventional there, because omitting it could cause readers to mistake “oriented” for a verb. If your publication’s style permits, you can follow CMOS 16 in omitting the periods: US-oriented.

Replace the hyphen by an en dash

There is another detail here worth mentioning, coming from the fact that Apple Inc. is a compound. With open compounds CMOS suggests, though doesn't exactly demand, replacing the hyphen with an en dash. In your case, that would be like this:

Apple Inc.–owned (en dash)

as opposed to

Apple Inc.-owned (hyphen).

Here's the relevant passage from CMOS:

(begin quote)
6.80: En dashes with compound adjectives

The en dash can be used in place of a hyphen in a compound adjective when one of its elements consists of an open compound or when both elements consist of hyphenated compounds (see 7.82). Whereas a hyphen joins exactly two words, the en dash is intended to signal a link across more than two. Because this editorial nicety will almost certainly go unnoticed by the majority of readers, it should be used sparingly, when a more elegant solution is unavailable. As the first two examples illustrate, the distinction is most helpful with proper compounds, whose limits are made clear within the larger context by capitalization. The relationship in the third example depends to some small degree on an en dash that many readers will perceive as a hyphen connecting music and influenced. The relationships in the fourth example are less awkwardly conveyed with a comma.

the post–World War II years
Chuck Berry–style lyrics
country music–influenced lyrics (or lyrics influenced by country music)
a quasi-public–quasi-judicial body (or, better, a quasi-public, quasi-judicial body)

A single word or prefix should be joined to a hyphenated compound by another hyphen rather than an en dash; if the result is awkward, reword.

non-English-speaking peoples
a two-thirds-full cup (or, better, a cup that is two-thirds full)

An abbreviated compound is treated as a single word, so a hyphen, not an en dash, is used in such phrases as “US-Canadian relations” (Chicago’s sense of the en dash does not extend to between).
(end quote)