If I recall correctly, it is explained that AI's in the Halo universe can take the shape or form of whatever they desire (usually a person of some sorts).
Deja, who was a "dumb" AI who helped teach the Spartan-II candidates, took on the form of a Greek goddess.
And then there are Serina and Cortana, who took on the forms of young woman (Cortana took the appearance of a 20-something year old Halsey, since she was her creator); and Roland, who took the appearance of a WWII pilot. I guess they do this for personality/distinguishing purposes?
And then there are a few AI's like Black Box, who argue against the idea of displaying as a person, since AI's are not real. As his name suggests, BB's avatar was simple a square box. There is also Auntie Dot, who simply appeared as lines and dots; and Superintendant, who is basically a voice over intercoms and security systems.
IRON MAIDEN IS MY RELIGION! Gamertag: Demigod Elessar
The A.I's are Halo's answer to the droids in Star Wars.
(The next few paragraphs are my own theories and opinions and not necessarily canon to Halo or the Star Wars universe)
The droids in Star Wars have A.I 'personality quirks' that are unintended by their creator (however tend to reflect their creator's moral alignment).
It gives the droids a personality, without actually making them a 'person'. Since the personality of the droid is unintended, or at least not specifically programmed; and also an indirect result of their 'wiring'; the droids personality is simply an unpridictable random mechanical occurance influenced by how it was built.
I kinda think the same goes for Halo's A.I's. They are created without personalities, but their 'wiring' tends to influence or engender one regardless.
This of course makes us the audience or players better able to relate to them as characters; and is actually a very brilliant writing mechanic.