"HAM" is a direct translation of the word "ham," and there are many theories and legends about how the term "HAM" refers to amateur radio enthusiasts. Therefore, it's likely that no one can definitively say which (one or more) is correct.
These theories and legends can all be traced back to the era when "Morse code" was the only method of communication via "radio," which was in its early stages. At that time, there were no regulations regarding radio frequencies, and amateur operators could use any available frequency and choose their own call sign.

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 amateur radio station used a call sign that was identical to that of a Mexican-registered ship called "MYALMO," causing confusion during communication. The operators were forced to change their call sign to the first letter of their last name, resulting in the call sign "HAM." At this time, as amateur radio was just emerging, there were no regulations regarding frequencies, and amateur stations could freely use any frequency and choose their own call signs. In some cases, the performance of amateur radio stations was even superior to that of professional stations. This situation drew the attention of the U.S. Congress, which began planning to enact strict regulations to suppress amateur radio stations.
One of the members of the "HAM" amateur radio club, named Herman, chose a controversial draft of wireless regulations from 1911 as the topic for his graduation thesis. Herman's advisor was also a member of the committee drafting the regulations, and he submitted a copy of his thesis 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 operations of amateur radio clubs, expressing his 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. This would force many capable amateur radio clubs to close, preventing them from continuing their research in wireless technology and indirectly hindering its development. Herman's presentation garnered significant attention.
Soon after, the bill was submitted to Congress, and the "HAM" amateur radio group, of which Haman was a member, became the focus. In this period, which was marked by uncertainty and controversy, "HAM" emerged as a threat to large commercial or professional radio stations that sought to suppress amateur radio. As such, "HAM" came to represent support for amateur radio, and Americans began using the term interchangeably with "amateur radio operator." This practice has continued from that year until today, and remains common in the radio industry.
This historical period is still preserved in the archives of the United States Congress. The achievement was hard-earned, and the importance of adhering to regulations is undeniable. Regardless of how the term "HAM" for amateur radio originated, or the contributions of Harvard University's "HAM" radio station, or even the entire development of radio, it deserves recognition from all!
However… what a pity!
The Harvard University Wireless Club website released a public statement: Over the past 90 years, this story has been repeatedly told and passed down through word of mouth. Unfortunately, "the facts don't support it." HWC members researched the story, even obtaining copies of congressional records related to the dates mentioned. We were unable to find any record of Mr. Lehman attending Congress. However, we must admit that it is a very interesting story!

Reposted from the Harvard University Radio Club website instructions.
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, these original meanings have completely disappeared."

Copied from ARRL's explanation of HAM radio
Option 4: Other possibilities
The Wikipedia article on ham radio provides some other theories that you can review to learn more about.
If anyone else with a HAM license can find additional explanations, please collect them and share them for reference. DE BD3OOX, 73!