Introduction
This is BD3OOX. I have searched through relevant websites worldwide and combined related articles from both domestic and international sources, summarizing and citing the following content. Please point out any inaccuracies.
Main body
"HAM" can be directly translated as "ham," and there are many theories about how the term "HAM" is used to refer to amateur radio enthusiasts. Therefore, it's likely that no one has definitively determined which (one or more) of these theories is correct.
All of these theories can be traced back to the era when the only way to communicate wirelessly was through Morse code. At that time, as wireless communication was in its infancy, there were no established frequencies for radio, and amateur operators could use any frequency they chose, along with their own call signs.

Here, we discuss some theoretical information that can be found globally, without any absolute data to definitively prove which one is correct.
Statement 1: Abbreviations of some early surname words
As far back as 1908, when amateur radio was just beginning to emerge, there was a group at Harvard University called the "Harvard Amateur Radio Club," consisting of Elbert S. Hyman, Bob Almay, and Paggy Murray. Initially, they used their own surnames as call signs: HymanAlmay Murry. However, they found this too long and cumbersome, so they shortened it to HYALMU.
In early 1909, the call sign used by this amateur radio station was accidentally identical to that of a Mexican-registered ship called "MYALMO," causing confusion during communication. As a result, the station had to adopt a new call sign based on the first letter of its owner's last name, and it became known as "HAM." At this early stage of wireless technology development, there were no specific regulations regarding frequencies, so amateur radio operators could freely choose their own call signs. In some cases, the performance of amateur radio stations was even superior to that of professional ones. This situation drew the attention of the U.S. Congress, which began planning to establish strict regulations to suppress amateur radio stations.
One of the members of the "HAM" amateur radio club, named Herman, chose as his thesis topic a controversial draft of wireless regulations proposed in 1911. Herman's advisor was also a member of the committee drafting the regulations, and he submitted a copy of his paper to a member of parliament named David I. Walsh, along with lobbying efforts. Walsh, impressed by Herman's work, invited him to speak before the committee. In his presentation, Herman detailed the operation of amateur radio clubs, expressing concern that strict regulations would stifle this popular activity due to the inability of many clubs to afford licensing fees and comply with various restrictions. He argued that this would force many talented amateur radio operators to close down, preventing them from pursuing research in wireless technology and ultimately hindering its development. Herman's presentation garnered significant attention.
Soon after, the bill was submitted to Congress, and "HAM," the small amateur radio station belonging to Hyman, became a focal point. Subsequently, "HAM" became a symbol of support for amateur radio stations against larger commercial or professional stations, particularly during a period when there were efforts to suppress amateur radio. As a result, Americans began to equate "HAM" with amateur radio operators, and the term has been used to refer to them in the radio community ever since, from that year until today, and into the future.
This historical period is still preserved in the archives of the United States Congress. The achievement was hard-earned, and requires everyone to abide by the regulations. Regardless of how the term "HAM" for amateur radio originated, or the contributions of Harvard University's "HAM" radio station to amateur radio development and planning, it deserves recognition from Wuhan residents!
Please pay special attention to
The Harvard University Wireless Club released a public statement regarding an old website version: "This legend, which has been passed down through countless stories and word-of-mouth accounts over the past 90 years, is not true. HWC members have researched this story and even obtained copies of congressional records related to the dates mentioned. However, we cannot find any record of Mr. Lehman attending Congress. Nevertheless, it is a very interesting story!"

Interpretation 2: "amateur" as an abbreviation
Some speculate that "ham" is simply a shortened version of the word "Amateur." "Amateur" becomes "Am," which then becomes "ham."
Interpretation 3: Derogatory terms for professionals
ARRL (American Radio and Electronics Laboratory) defines "HAM" as: "In the early days, each station occupied a very wide bandwidth signal across the entire spectrum. Government stations, ships, coastal stations, and an increasing number of amateur operators were all vying for spectrum resources. Many amateur stations were very powerful. Two amateurs communicating in a town would interfere with all other communications in that area. Disgruntled commercial operators referred to them as "hams," using the term to refer to ham radio interference. This is because professionals would call any amateur operator who was not particularly skilled, whether professional or otherwise, a "ham-fisted" (i.e., clumsy; inept). Of course, at least from the perspective of professionals, amateurs were never good people. Those amateurs who did not fully understand the true meaning of the term picked it up and applied it to themselves. Over time, the original meaning has completely disappeared."

Option 4: Other possibilities
The Wikipedia article on ham radio provides some other theories in its etymology.
If anyone else can find additional explanations related to this, please collect them and share them for everyone's reference.