The Ajna is the one centre in the Human Design bodygraph that kept its Sanskrit name, and the naming is the clearest single sign of where the nine-centre scheme came from.
The name
In the classical chakra scheme, ajna is the brow centre, the sixth of the seven counting upward. Human Design places a centre in the same position and uses the same word for it, where every other centre in the bodygraph carries an English name.
The arithmetic of the borrowing
The classical scheme usually cited in modern Western usage has seven centres. The bodygraph has nine. Two of the nine, the G or Identity centre and the Spleen, have no classical counterpart and are additions. The remainder correspond by position, with varying closeness of function.
Human Design does not claim to be a chakra system, and describing the relationship as an adaptation with two additions is more accurate than describing it either as a transmission or as an unrelated invention.
A caution on the other side
The sevenfold scheme is itself one arrangement among several. Indian tantric traditions describe systems with different numbers of centres, and the standard seven of modern Western usage is a settled popular version rather than a single original. The comparison above is between a 1987 construction and that popular version.
Human Design was published by Ra Uru Hu in 1987 and is recorded here as a contemporary system rather than as inherited material.
Sources Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland with The Origins of Yoga and Tantra: Indic Religions to the Thirteenth CenturyGeoffrey Samuel, The Human Design SystemRa Uru Hu (Alan Robert Krakower)