what type of property
Turbotax should be selecting the best method based on what you entered for the type of asset.
buildings are depreciated using the straight-line method and mid-month convention over 27.5 years for residential real estate and 39 years for commercial - types I and J1
It is a residential rental so it should be 27.5. It accurately gets the 27.5 but then it does SL/MM. I acquired this property late in the year (October) and I'm trying to depreciate at half a year DD/HY. How can I change the method and convention?
Sorry but it doesn't work that way ... a residential use building cannot use the DD/HY method ... the ONLY option is the SL/MM method that the program does correctly automatically.
I agree with @Critter-3 , for what that is worth.
You cannot use an improper method and TurboTax is selecting the proper one. This can be subject to an override in the program but you would do that at your own peril.
As a side note, I do not quite understand why you might possibly believe that putting residential rental real estate in service late in the year would give you an option to select a different method of depreciation.