This is indeed a perplexing question that has come up from time to time, going WAY back! The practical, and rather boring, explanation is that Monogram Pictures probably wanted to keep "Tommy" in the picture after the departure of Benson Fong and the return of Victor Sen Yung. Perhaps they felt that audiences had gotten used to having the Tommy/Birmingham pairing.
Charlie Chan fans have come up with their own theories in attempts to "explain" the shift and name retention and thus restore a sense of continuity. The most accepted explanation, and the one I personally subscribe to is the following. With the beginning of the Roland Winters phase of the Chan series, neither Number Three Son, Tommy nor Mrs. Chan are ever mentioned again. (Tommy Chan was last heard from in "Dangerous Money," when his famous pop communicated with him by cablegram while sailing the South Seas with son, Jimmy.)
You have noted that Victor Sen Yung's "Tommy" is referred to as "Number TWO Son." This could indicate that, for some reason, Jimmy has taken on his younger brother's name. Continuing with the "theory," it seems that both Mrs. Chan and Tommy might have met with some sad event resulting in their joining their illustrious ancestors. Due to the nature of his brother's demise, Jimmy took his brother's name as something of a tribute. This could have been to also ease the pain that his father experienced at not only loosing a son, but his venerable wife as well. This could also explain why Charlie Chan is "suddenly" based in San Francisco, away from his beloved Honolulu.
So, there you have it: "Reality" versus "Romantic." As I said above, I prefer to follow the more fanciful, "romantic" explanation, which would serve restore a slight break in the continuity of the Charlie Chan film series. Other "theories" could also be formulated to fill this gap, of course!
Audience familiarity with the Tommy/Birmingham pairing is the most likely explanation, and the number two son/number three son confusion was probably just an overlooked error.
Your off-screen death explanation actually adds depth to the characters. It made me think of a true-life story about the young Katherine Hepburn, who assumed her beloved teenage brother's birth date after he committed suicide.
My own favorite theory, as of two minutes ago, is a multiverse of many earths (courtesy of TV's The Flash) -- with each change of actor playing Charlie Chan we're actually looking at a different earth, similar to but significantly different from the earth that came before, so on Roland Winter's Charlie Chan earth there never was a number two son named Jimmy, just a number two son named Tommy who looks like Jimmy from Sidney Toler's Charlie Chan earth...
Now I'm just being ridiculous. Thanks again for the reply.
As I, too, am familiar with the "multiverse" as seen (hugely!) in "The Flash" TV show, your suggestion in that direction is a fun take. I was not aware of the Katherine Hepburn angle. Thank you for sharing that!
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My personal theory is that the actor Sen Yung had a bond with Toler and only wanted to be "Jimmy" for Toler. When Toler passed he retired the Jimmy character and became Tommy perhaps retaining #2 status as a compromise.
The Chan films were very popular and even though Monogram was a poverty studio they still employed good writers. I can't believe it would have been an overlooked accident to change character names without reason. After all, Yung was "Jimmy" in the last batch of Toler films. There would have been a whole slew of people who would have noticed the change before cameras started rolling.
Yours makes sense as a possible answer. I agree that the name change was certainly not an "accident" as Victor Sen Yung probably asked the big question regarding this when he first read the script for what would in the end be titled "The Chinese Ring" (working titles: "The Mandarin's Secret" and "The Red Hornet"), the first Roland Winters Chan picture. In the end, calling Jimmy "Tommy" was probably an executive decision.
