Fortunately there's little need for guessing, it's all available in print.
Ella started touring with the band as early as July 6, 1939 under the billing "Ella Fitzgerald and Chick Webb's Famous Orchestra".
First, they had a one-week engagement at Loew's State Theatre in New York City (see image above). From there, they went on to a six-week engagement at the Savoy Ballroom in New York City, starting on July 16, 1939 (all info, including two photos of contemporary newspaper ads with this orchestra name, from Ron Fritts & Ken Vail, "Ella Fitzgerald: The Chick Webb Years & Beyond", p. 45).
By September 1939, Decca had released a Chick Webb Memorial Album, Decca Album No. 138, reviewed in the Sept. 1939 issue of "The Gramophone", p. 166. It contained 6 previously released records under their original catalog numbers:
483 Don't Be That Way/It's Over Because We're Through 1220 You Showed Me The Way/Clap Hands! Here Comes Charley!
1840 A-Tisket A-Tasket/Liza
3318 On The Sunny Side Of The Street/Undecided
3319 Sing Me A Swing Song/A Little Later On
3320 The Dipsy Doodle/In A Little Spanish Town.
All this shows that Ella, even though she was only 22 years old, didn't need much time to establish herself as the orchestra's new leader. But for about three months, while everyone bought Chick Webb mementos, it made economic sense to remind people that the orchestra was still the same he had led, even if Ella was now its leader.
Two weeks is hardly any time for anything to have been settled unless arrangements had already been made in anticipation of Webb's imminent demise. That's not at all impossible, but it is something of which I have no direct knowledge. If I had to guess, I would say that the session had already been scheduled while Chick was still alive. It probably had not been finalized when it came time to issue the disc that the orchestra name would be changed, so it went out under Ella and Webb's name together. (They could, of course, also have wanted to capitalize on his name for a bit longer, just as you said, xiphophilos.) In any event, once Ella's succession to the leadership role had been established, it would have been appropriate to change the label on subsequent pressings to reflect the fact. I would think that Ella would have compelling reasons to want that in any case once she started touring with the band under its new name.
If the recording date I found on 78discography is correct, these sides were recorded 13 days after Chick Webb's death on June 16, 1939. So at this point, Ella has already taken over the orchestra. I assume she (or the record company) is still trying to capitalize on Chick Webb's name.
The illustrated labels are most likely the earliest version of this disc issued. Another version is extant where the artist credit has been changed to Ella Fitzgerald and Her Famous Orchestra. I would assume the change happened after Chick Webb's untimely death and the orchestra passed to Fitzgerald's leadership.