It´s indeed complicated to get these right, the parent company has changed name several times as you point out and in sales material the copywriters also change order in which the name comes. So it´s a bit confusing.

I havn´t looked into this much earlier, but as brand name the Willys-Overland Motor Company used only Willys both on their cars and the Jeeps. This didn´t change, as far as I can see, when Kaiser bought the company in 1953. The company became Willys Motor Company instead and was again renamed 10 years later to Kaiser Jeep Corporation.

In advertising it seems to be a change in brandname already in 1955, from Willys to Jeep. When the CJ-5 was introduced it had only the name Jeep on the body, and later models introduced like the Forward Control Truck [FC-150] and [FC-170] and the Wagoneers carry only the Jeep nameplate and are named nothing else in advertising.
The only exception I have found after 1954 is the CJ-3B, it still wears the Willys name stamped on the hood. I would guess that it was considered too expensive to retool for this old model.

I´m sure this can be debated since the parent companys name almost always appear in the ads, but comparing to the car side of the company you can also see that the Overland part is never used on a vehicle after the mid twenties, with a brief exception in 1939 as a modelname. And when car production ends in 1955 it seems that they drop the Willys name even on the Jeeps.

Some samples:

1945:
http://www.oldcaradvertising.com/Jeep%201944-53%20Ads/1945/194520Ad-02.html
http://www.oldcaradvertising.com/Jeep%201944-53%20Ads/1945/194520Ad-06.html


1953:
http://www.oldcaradvertising.com/Jeep%201944-53%20Ads/1953/195320Ad-02.html

1954:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1954/195420Ad-01.html
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1954/195420Ad-03.html
Willys Station Wagon
http://www.oldcaradvertising.com/Jeep 1954-69 Ads/1954/1954 Jeep Ad-03.html

1955:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1955/195520Ad-02.html
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1955/195520Ad-05.html
The Willys Station Wagon became the Jeep Station Wagon
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1955/195520Ad-04.html

1957:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1957/195720Ad-05.html

1959:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1959/195920Ad-01.html
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1959/195920Ad-04.html

1962:
http://www.oldcarbrochures.com/static/NA/Jeep/1962_Jeep/1962_Jeep_Full_Line_Broc- hure/dirindex.html

1965:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1965/196520Ad-03.html
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1965/196520Ad-08.html

1969:
http://www.oldcaradvertising.com/Jeep%201954-69%20Ads/1969/196920Ad-01.html

1971-72:
http://www.oldcaradvertising.com/Jeep%201970-87%20Ads/1971/197120Ad.html
http://www.oldcaradvertising.com/Jeep%201970-87%20Ads/1972/197220Ad-0b.html