"As we called them" in this context means "what we called them", and in this specific example, the last two places (towns or villages) were Taza and Tamri, so they named the two donkeys the same as the names of those towns or villages.

The meaning is probably "like" or possibly "because". It is not clear because the sentence is not grammatically correct. This would be correct: a) Taza and Tamri, who(m) we called after the last places in the trip, well, they made quite a unique journey... b) Taza and Tamri, as we called them (they were the last places in the trip), well, they made quite a unique journey.... I suspect the writer is a native speaker but they did not check their grammar well here.

Here, "as" is a preposition. It refers to the function or character that something has: - She got a job as a bus driver. - I was treated as a family member. - The news came as a shock. Let's divide this sentence up at the commas: - Taza and Tamri, => names - as we called them after the last places in the trip, => with the names Taza and Tamri, this forms an introductory clause - well, => "filler" word indicating a pause but without particular meaning - they made quite a unique journey between them, => main clause - and . . . but it was continuously demanding for them => second sentence joined to the first sentence by the conjunction "and" If we ignore "well" and everything after and," we get somewhat simpler sentence: - Taza and Tamri, as we called them after the last places in the trip, they made quite a unique journey between them... Introductory clause: - Taza and Tamri = names - as = preposition referring to the function (names for the donkeys) that "Taza" and "Tamri" serve here - we = subject - called = named - them = pronoun referring to the two donkeys in the previous sentence - after = in allusion to, in honor of - the last places in the trip = the final places we had been to on our journey Main clause: they = the two donkeys, Taza and Tamri made = had, took, traveled upon quite = adverb meaning "completely" a unique journey = here, unique probably means "remarkable" between them = I think that in this context, "between them" means "together." So, putting it all back together: - Taza and Tamri, which is what we named the two donkeys in honor of the final locations we had seen on our journey, they took a completely remarkable journey together... I confess that I don't know exactly what the author means by "quite a unique journey." I think it's a very old-fashioned piece of British-style understatement/irony/sarcasm for "an absolutely harrowing and awful journey," but native speakers of British English are invited to correct and properly inform me.