How would you calculate the true anomaly of a circular orbit (e=0)? I'm trying to design an orbit for a mission on STK and so I'm not sure what the eccentric anomaly (in order to calculate true anomaly) would be since it's not a question about the orbital element at a particular time.
For your own calculations, whenever you have a case of zero (or very small) eccentricity you may need to handle them differently and just choose an arbitrary argument of periapsis, perhaps zero.
What does "very small" eccentricity mean for you? Small enough so that it doesn't make a difference (your orbit doesn't deviate from a circle by more than your acceptable error) or so small that it causes other numerical issues.
Then just use $𝜈=𝑀=2𝜋/𝑇$
Fig. 1: Diagram of orbital elements, including the argument of periapsis (ω).