What is it called when two words are combined by overlapping each other?

Say I have the word "hotel" and "telephone." I then combine them together to make "hotelephone." Note that there is no truncation in this example. It is not a portmanteau. I have seen multiple examples of this, sometimes when people make very long strings of intermeshed words. I thought of the word for it earlier, but now I've forgot, and I'm totally stumped. It seemed like a question for an English stack exchange.

In computer science, a word that contains other words (hotelephone and hotelephone, both words are present) is called a

superstring.

Your example happens to be the shortest common superstring of hotel and telephone; there is no word shorter than hotelephone that contains both hotel and telephone. It's an interesting problem to compute shortest common superstrings.

Note that in your example, one "-tel-" from the two is dropped, so there is truncation. If there were no truncation, then your word would be a compound word.

Describing the term portmanteau, Wikipedia says:

A portmanteau (/pɔːrtˈmæntoʊ/, /ˌpɔːrtmænˈtoʊ/) or portmanteau word (from "portmanteau (luggage)") is a blend of words in which parts of multiple words are combined into a new word, as in smog, coined by blending smoke and fog, or motel, from motor and hotel. In linguistics, a portmanteau is a single morph that is analyzed as representing two (or more) underlying morphemes.

This term is different from contractions or compound words:

A portmanteau word is similar to a contraction, but contractions are formed from words that would otherwise appear together in sequence, such as do and not to make don't, whereas a portmanteau is formed by combining two or more existing words that all relate to a single concept.

A portmanteau also differs from a compound, which does not involve the truncation of parts of the stems of the blended words. For instance, starfish is a compound, not a portmanteau, of star and fish, as it includes both words in full.

M-W sheds more light on this phenomenon:

In Lewis Carroll's Through the Looking Glass, Alice asks Humpty Dumpty to explain words from the nonsense poem "Jabberwocky" and is told that slithy is "like a portmanteau-there are two meanings packed up into one word." Although slithy hasn't caught on (it's made up of slimy and lithe, according to Humpty Dumpty), another portmanteau invented by Carroll has in fact found a place in the language: chortle (supposedly from chuckle and snort).

English includes other portmanteaus, too, such as brunch (breakfast and lunch) and dramedy (drama and comedy). Following Carroll's lead, English speakers have come to call these fairly common words by the not-so-common name for a type of traveling bag with two compartments. The technical (and simpler) term for such words is blend.

haplologic/overlapping blends

From the sources below, it appears that overlapping blend is a subtype of haplologic blend.

A blend (sometimes blend word, lexical blend, portmanteau or portmanteau word) is a word formed from parts of two or more other words.
...
Overlapping blends are those for which the ingredients' consonants, vowels or even syllables overlap to some extent. The overlap can be of different kinds. These are also called haplologic blends

There may be an overlap that is both phonological and orthographic, but with no other shortening:

anecdote + dotage → anecdotage
pal + alimony → palimony
... Wiki

Haplology is a name given to syllable suppression due to repetition of sound. When two successive syllables have their prominent elements in common, syllable syncope is likely to ensue. Haplological blends would then be forms in which one part of the compound is eliminated because it occurs in another part. Blends—Their Relation To English Word Formation (2014)

One of the examples given in Blends (in addition to Wiki's anecdotage) is alcoholiday, in which, like the OP's ho[tel]ephone, both overlapping words are present in their entirety: alco[hol]iday.

Another type [of error] includes "Haplologies and other Telescopic Errors" ...i.e. when a word is shortened or two words are merged by deleting one or more syllables or syllable parts to ease pronunciation. Haplology generally occurs when two words are blended where they overlap, as in muddle←mud puddle, or nitness←Nixon witness. Overlapping blends, such as adaptitute [1806) adapt + aptitude (OED3), or affluenza [1973]← affluence + influenza ... could have their origin or model in spontaneous phenomena like the above-mentioned haplologies. Analogy in Word Formation (2017)

haplology
contraction of a word by omission of one or more similar sounds or syllables (as in mineralogy for hypothetical mineralology or \ˈprä-blē\ for probably)

American philologist Maurice Bloomfield recognized the tendency to drop one of a pair of similar syllables a little over a hundred years ago. He has been credited with joining the combining form "hapl-" or "haplo-" (meaning "single") with "-logy" (meaning "oral or written expression") to create "haplology" as a name for the phenomenon. m-w

As others have stated, I believe your assertion that it not a portmanteau is incorrect.

Tom7 has a video describing portmanteaus and takes it to the extreme by creating one containing every word in English.