The Dahlander motor refers to a specific set of optional connections to the main stator winding. These are done OUTSIDE the motor frame (or at least within the main terminal box).
This gives a single pole count for the motor, and the VFD can effectively control the machine as if it were not capable of multiple connections.
The VFD - by itself - cannot "switch" the lead connections to achieve a different pole count. However, it can modify both the applied voltage and frequency - which gives a similar result.
The fact that a Dahlander connection is a speed ratio of 2:1, and whether one connects it in the low or high speed connection for VFD operation - given that only one speed will apply for VFD operation.
In this respect - the recommendation would be to connect the motor in the low speed connection. All of GoHz VFDs will operate to 100 / 120 Hz without issues, so the higher motor speed will be achievable with ease via VFD with the Dahlander winding in the lower speed connection. This will give higher starting torque and better torque control over the full speed range of the traditional motor connection without VFD supply.
One exception to this is if you do not require high starting torque. In this case the higher speed connection will normally provide better inherent motor performance and then you should connect the winding in the high speed configuration.
Also be aware that the 2 speed Dahlander motor normally has two different power ratings for the two speeds. The lower speed generally has a lower power rating than the higher speed. However the lower speed often has a higher torque rating than the higher speed. When operating on a VFD, plot on a graph the various expected operating points, then decide which of the two base speeds to select for your VFD connection.
Two speed (Dahlander) motors are still in common usage despite availability of VFDs. In generator cooling radiators, there are often multiple cooling fans with 2 speed operation because this is reliable and low cost.
If the radiator is designed for maximum ambient temperature and generator maximum output, then the majority of time there is more cooling than needed. With all fans running at full speed, the power consumed by the fans can be significant % of the generator output (up to 6%). Reducing fan speed to half, will reduce power consumed to 1/4 of full speed but provide about 75% of cooling capacity. The generator will spend most of the time at less than maximum ambient temperature and less than full load, so there is a majority of time when the fans can be at half speed.
The same effect is available with VFD on the fans, but there is a concern if you have one VFD driving all fans, this is a common point of failure. Purchasing one VFD for each fan can be expensive.