For single pilot VFR operations, unless the aircraft is certificated as requiring 2 pilots, FAR 135.105 does not require 2 pilots OR, in the alternative, a 3 axis autopilot in lieu of 2 pilots.
Exceptions to this are shown in 135.99 (e.g., using an aircraft with 10 or more passenger seats) and 135.111 (Cat 2 operations).
135.105 must be read along with 135.101 (135.101 requires a second in command for IFR passenger carrying operations). 135.105 allows an exception/alternative to the 2 pilot requirement specified in 135.101. Specifically, unless the aircraft requires 2 pilots under VFR, a 3 axis autopilot can be used in place of the 2 pilot requirement specified in 135.101 (IFR passenger carrying operations).
Specific to the 3 axis autopilot issue, I don't think a yaw damper in every case meets the requirements to be one of the 3 axis autopilot components. The technical specifications that accompany the aircraft certification data which incorporates a 2-axis auto pilot with yaw damper should be consulted for guidance.