The 0.5A is irrelevant (as long as it's sufficient). The voltage difference over the regulator is in combination with the required current.
The regulator on the nano will dissipate (convert to heat) 150mA * (12-5) = 1 Watt.
I have no idea what the nano design can take; personally I would simply test by putting a finger on the regulator and check how hot it gets. But that's a subjective measurement.
I want to increase the output voltage of an PWM Singal up to 10V.
So I want to put the opv to the same voltage source like my Nano is.
On account of that I need a minimum voltage of 10V.
I want to achieve that by using an DCDC-Converter.
I want to convert an Voltage from 24V down to 10.
First you say you want to go to 10V for some amplified PWM but you link a 5V DCDC.
As the datasheet says, the TDR can do 600mA (@80% efficiency). So fine if you indeed use 150mA. At the 24V it will draw 150mA x 5V / 24V x 100% / 80% = 39mA.
But that is if you use a DCDC to 5V. 150mA for the regulator on the Arduino to go from 10V to 5V is already a bit to much I think. It's pretty small and needs to dissipate 150mA x (10V - 5V) = 750mW. I think that's a bit much for it.
But what do you need to drive @ 10V? If that's low power it's easy to use a DCDC for the 5V and a linear regulator for the 10V.