This is a relatively rare word! It has only one result in BCCWJ, and I couldn't find a definition for it in any of the seven monolingual dictionaries I checked. However, I did find it mentioned in the definition for 熟す in 明鏡国語辞典, where it's given as a synonym:
Here's my translation of the relevant passage:
To put two words together inseparably, forming an idiomatic word or expression. Or, for a new word to become widely used.
As you can see, 熟合 is related to 熟す(る) and to 熟語／熟字, words I bet you're more familiar with. I think Eiríkr Útlendi's gloss of idiomatization captures this idea relatively well. It expresses that the combination is non-compositional, which is to say, the meaning may not be predictable from the pieces that were put together.
A related English term is lexicalization, where a new lexical item is formed, requiring its own dictionary entry because its meaning can't be synchronically derived from a simple combination of other lexical items. For example, English traffic light is clearly the combination of traffic and light, but it needs its own dictionary entry because "A set of automatically operated colored lights, typically red, amber, and green, for controlling traffic at road junctions and crosswalks" isn't something you can predict from those two words alone.
However, in this particular example we're talking about a morphological structure rather than a lexical item. And in this case, morphologization may be more appropriate:
In morphologization "[P]honological processes and syntactic structures [...] become properly an aspect of morphological, rather than phonological or syntactic, organization" (Fox 1995: 102). As pointed out in the previous quote the two sources morphologizied structures can originate from are the phonological and the syntactic domain of grammar. Those two types of morphologization have also been labeled dephonologization and desyntactization respectively (Joseph 2003: 473).
Another related term is fusion, the combination of two forms into one. This is the term used in Frellesvig's 2010 A History of the Japanese Language to describe the formation of -kar- (p.40):
Another similar set of forms are those where the existential verb ar- seemingly fuses with a preceding grammatical monosyllabic morpheme: the periphrastic stative -te-ar- giving -tar-, the extended negative -(a)zu-ar- giving -(a)zar-, and the extended adjectival copula -ku-ar giving -kar-. In these cases, however, ar- must be thought to fuse with the full inflected form, not just the suffix: kakite-ar- ⇒ kakitar-, kakazu-ar- ⇒ kakazar-, akaku-ar- ⇒ akakar-. In OJ all such forms were simple phonological fusions (220.127.116.11.2), but in EMJ they were reanalysed to give rise to the morphemes -tar-, -zar-, and -kar- (8.2.1).
So we could use this term in English, but fusion doesn't describe an accompanying change in meaning, only a change in form. Searching online for 熟合, we find people often talk about the process in terms of an accompanying change in meaning. For example, this blog post:
Or another similar example:
So I think your guess "combine, merge" is pretty close, but 熟合 may also imply an accompanying change in meaning.