TurboTax gave me a depreciation value for my new tuck (08/05/2020). Will turbotax change that value for me next year? Or will i have to calculate it next year?

No, you don't need to calculate the depreciation next year. TurboTax will automatically make the calculation based on how many month you are using the truck for the business as long as you use the same TurboTax account that you are using this year.