Elites can obviously tell each other apart fairly easily. The don't walk around with name tags. "My name is: Thel Vadam"

if:

• children look like the father
• females produce eggs after a predictable time after intercourse

The only way that the Sangheili system could work would be if Sangheili males were pretty dim or the two conditions above didn't hold.

How could they not hold?

• identifying features are inherited from the mother
• the females can store sperm until they are ready to start laying

Females could decide as a group when to start a communal clutch of eggs.
Females may practice cryptic female choice; they could degrade sperm of mates that don't impress them; they can control blood lines (isn't that their job in Sangheili society?)

Ignoring venereal disease: males and females could mate as often as they like with multiple partners and the females decide which males quicken their eggs.

And since everybody is doing it with everybody it would be hard for the males to keep track of which child was whose.