I'm using a buck converter to go from 7.5 volts to 5 volts to power a servo. Does the ground from the buck converter that goes to the servo also have to go to the Arduino board ground pin as well?
Yes, to provide a current flow path for the arduino servo control signal to go back to the arduino. Your servo will also probably work better at 6v than 5v.
“Buck” converters generally have the ground pin for the output the same as for the input.
Somewhere, the ground for the Arduino must connect to the ground on the servo and in general the control and ground wires should run together as a pair.
What are you using to power the Arduino? If you are using a Buck converter to power the servo at 5V, the same 5 V can - and generally should - power the Arduino via the “5V” pin but you should ensure there is at least a 1 mF capacitor between that 5V pin and ground for bypassing.
If the Buck converter is providing 6 V to the servo, then you cannot use it directly to power the Arduino but you could put a power diode (1N4004 etc.) in series with the 1 mF capacitor afterwards to power the Arduino at 5.4 V. (Do not connect this however while the Arduino is connected to a USB port on a computer.)
Note the general understanding: All circuit wiring, power and ground and control and ground, should run together from one part to another, paired, using “figure 8” or ribbon cables. If using separate wires, they should be tied together or possibly twisted. You should not leave open loops between one wire and its corresponding ground.