tuningste, I think I understand your question now.
There is only one GND, not two. The digital potentiometer is not isolated from the Arduino, so there is only one GND.
The RH and RL of the digital potentiometer can be used to set the digital potentiometer for example between 3V and 12V. However, it needs to be between 0V and 10V, so RL must be connected to GND.
Since there is only one GND, a isolated DC/DC-converter has no extra advantages, just a DC/DC-converter will do.
If you have already that DC/DC-converter, you can use it to power the Arduino.
It is not advised to power the Arduino via the VCC pin, but it will work if the DC/DC-converter is weak. Smashing a strong 5V onto the VCC pin can damage the voltage regulator with a reverse voltage. When the Arduino is connected to a computer and that computer is turned off, then a current can flow from the fan via the DC/DC-converter via the Arduino into the computer. I have not destroyed a computer that way... yet.
The digital potentiometer will work, but you need the I2C bus and code or a library to control it.
So after all, the most simple solution is to find a library that can make a PWM signal above 1kHz for the Arduino and use a transistor as Wawa already concluded. When reading all the PDF files of the fan I saw a schematic, you need to add a resistor from the Arduino to the base of the transistor.
Now we are getting somewhere. When you use a isolated DC/DC-converter and a opto-coupler instead of a transistor, then you can isolate the fan from the Arduino. That is so much safer. Can you make a schematic for that so we can verify it ?
Please take your time to read the following:
You are looking at something and you know what you have, we don't.
Therefor you could have started with a photo of the fan and its wires, and telling exactly which type of fan it is. Then we have an idea what you are talking about.
You should give more links !
Did you notice that I gave links to the DS3502 and the ECblue fan ? That is your job, we are not a googling service.
I did not give a link to your Arduino board, here it is (Sparkfun Pro Mini): https://www.sparkfun.com/products/12640.
The first reply by ballscrewbob was the best reply. Did you read those links ?
Did you read at number 16 about the XY-problem ? http://xyproblem.info/.
You asked for the wrong solution. Your question should be: "How do I control a ECblue fan with an Arduino".
But no worries, we are all Arduino-enthusiasts and we are very patient. It took me a long time to learn how to ask a good question 