Is the word '여보세요' ('hello?') related to the word '여보' ('darling')? If not, where does '여보세요' come from?
여보 originated from 여기 보오 "look at here", and 여보세요, 여보시오 from "여기 보세요", "여기 보시오" respectively. They all mean "look at here", just differing by speech level.
The word was used in the early 20th century to address strangers(여보쇼 for older-looking people, 여보게 for younger looking people, 여보 for similar looking people). In fact the word was used so much on the street that the Japanese, who occupied the Korean peninsula at the time, disparagingly called Koreans "yobo"s. This explains why 여보세요 is the standard "hello" word in telephone speech. The dictionary also lists this usage as the primary one.
여보, 앞 좀 잘 보고 다니시오. Hey, look where you're going!
This word, 여보, was also used between married couples. Then the original usage, calling strangers, fell out of usage.(It got replaced by 여기요, 저기요 or 그쪽, etc) Nowadays it's commonly accepted as calling names between married couples by the younger generation.
There's also 여봐라, which kings used to call their servants.
I have heard it claimed that 여보세요 is short for "여보 계세요?" (Is your 여보 there). However, I do not think this is the actual meaning of the phrase 여보세요. A 75 year old man with lots of gold teeth told me this version, so take it with a grain of salt.
To my understanding, the real meaning of 여보세요 comes from a melding of the words 여기 (here) and 보다 (to look/see). 여보세요 takes on a meaning of "Look here" or "Look at this!"
I have read before that the reason why 여보세요 is used is because in the early days of the telephone, people were so impressed that they could talk across large distances that they would exclaim "Well, would you look at that!" (Rough English translation of the concept). This was eventually shortened to 여보세요. This too may be a version told only by elderly gentlemen with metallic teeth.
So, the majority answer here is that 여보세요 is a portmanteau of sorts of the words 여기 and 보다, and does not have any relation to one's darling or honey.