According to Wikipedia:
In 1975, Duplo became its own product brand, with five sets made up
exclusively of Duplo bricks.
In 1977, the Duplo name was dropped in favor of Lego Preschool.
The name Duplo was brought back in 1979, along with a new reworked
Although I haven't found this information yet (most people likely see this detail as unimportant), it is possible that LEGO started with putting DUPLO on the bricks either when they first came out (in 1969) or in 1975 when DUPLO became its own "product brand". They likely changed it in either in 1977 (when LEGO called it LEGO Preschool) or in 1979 (when they brought back the name DUPLO).
According to Brickipedia:
In the Preschool range, new DUPLO bricks were introduced, including arches and the first DUPLO figures, which did not have movable limbs.
Considering the above quote, it is possible that with the new bricks the DUPLO on the "knobs" (as you call them, however the proper name is a "stud") was changed to "LEGO"; this was in 1977 on.