What is the term for "‑ate" noun/verb pairs, and why can’t I find references to "hyphenate" used that way?

Solution 1:

If you had used phonetic notation, the answer would have been completely apparent.

The first pronunciation in each pair below is the verb; the second is the noun or adjective, or both:

• conjugate /ˈkɒndʒʊˌɡeɪt/ vs /ˈkɒndʒʊɡət/

• ruminate /ˈruməˌneɪt/ vs /ˈrumənət/

  ^{John Lawler notes in comments that the noun ruminant means something else. However, there is a rare adjective ruminate used in botany.}

• hyphenate /ˈhɑɪfəˌneɪt/ vs /ˈhɑɪfənət/

• concentrate /ˈkɒnsənˌtreɪt/ vs /ˈkɒnsənˌtreɪt/

  ^{(The alternate /kənˈsɛntrət/ pronunciation of concentrate given for the noun and adjective by the first edition of the OED is now uncommon at best, and is mentioned only in passing in the third edition.)}

In other words, this is the familiar pattern in English of stressed vowels not reducing but unstressed vowels indeed reducing. The verb has a stressed (or at least unreduced) /e/ phoneme in the final syllable, whereas the noun or adjective in losing its stress, reduces to the standard reduced /ə/.

As for why you can’t find hyphenate as a noun, you may be looking at abridged dictionaries. The OED mentions this early citation:

• 1922 Contemp. Rev. Dec. 693
  The ‘hyphenates’—Irish and Germans, Poles and Russians and Italians—..joined in the condemnation of Wilsonism.

As far as I can see, the verb enters the language first, and then some years later a corresponding noun (or occasionally adjective) appears via zero derivation (conversion to another part-of-speech without a change in spelling), and it is this substantive which suffers a reduction in its final syllable, since because it’s no longer a verb, we don’t much feel like retaining its stress. Compare reˈcord verb with ˈrecord noun.

There’s no special word for these pairs. You can think of them as verbs plus their (zero-)derived nouns if you’d like, respectively unreduced and reduced due entirely to contrasting stress patterns between the two.