Describing the phonetic interaction between the F and the T in often

I think the term you are looking for is assimilation:

• Assimilation has a very precise meaning when it’s related to studies of languages. Is a common phonological process bye which the phonetics of a speech segment becomes more like another segment in a word. In other words it’s when a letter (sound) is influenced by the letter (sound) before or after it so that it changes its sound and/or spelling. The word assimilation it self it’s said to be assimilated; it is derived from the latin prefix ad- meaning to and simil- meaning like but, instead of being adsimilated, it has the easier pronunciation of assimilated.

(phonetics-and-phonology)

Often: as explained in the following extract by James W. Bright:

• “often,” the word can be properly pronounced either with or without a “t” sound. The “t” had long been silent but it came back to life in the 19th century with the rise of literacy, when people seemed to feel that each letter in a word should be sounded.

• The article, “On ‘Silent T’ in English,” by James W. Bright, appeared in the journal Modern Language Notes in January 1886.

• As Bright explains, the “t” in these words is an acoustically “explosive” one, and to sound it after an “s” or an “f”—both of which expend “considerable breath”—is “especially difficult and obscure.” Consequently the “t” sound is assimilated into its surroundings and becomes silent.

• However, the “t” sound persists in some other words spelled with “-stl” and “-ftl,” like “lastly,” “justly,” “mostly,” “shiftless,” “boastless,” and others.

• Bright explains that such words “are, with most persons familiar with their use, conscious compounds; as they become popular words, and therefore subject to unstudied pronunciation, they conform to the regular rule. It is only after administered caution that we learn to make t audible in wristband.”

(grammarphobia.com)

The usual linguistic term for the complete loss of a sound is elision; in this case, the sound /t/ was elided when it came after a fricative and before a homorganic syllabic consonant [n̩] or [l̩] (which are usually analyzed phonemically as /ən/ and /əl/, and pronounced that way for some speakers).

The Concise Oxford Companion to the English Language describes the situation as follows (it's mostly concerned with the orthography, however, not the phonology):

[T is] elided after s following a stressed vowel: before /l/, especially in the terminal syllable -le, as in castle, nestle, pestle, trestle, wrestle, [...], rustle; before n, especially the terminal element -en, in chasten, hasten, fasten, christen, glisten, listen, moisten; and in isolated words such as Christmas, postman, waistcoat. (3) Elided after f in soften and often in often.

It may be worth noting that some of these words, for example "glisten", did not in fact originally have a /t/ sound in Old English; the fact that it is spelled with a "t" might be due to the sound change that occurred and the subsequent reanalysis of the spelling -sten as a representation of word-final /sn̩/, and -stle as a representation of word-final /sl̩/.