I wondered if it is possible to set the output filename of FASM different to the input filename. This maybe possible with command line version but I am using the FASMW version as IDE and it wouldn't be bad to set the output filename with some statement different from the compiled name.

With format as "..." I can only change the extension.
So is there a statement to set a full output filename ?
I am not sure, so I am asking the experts.

I am looking for an easy way for a presentation to have different input files but one and the same output file which is processed further and overwritten new with each input file loaded.

No, you can do it only in console versions of FASM.

FASMW is very minimalistic IDE and such feature can not be easily implemented. I mean, the name of the binary file is a property of the project, but FASMW does not support projects.

If you need this feature, you can use the command line compiler, or Fresh IDE which supports project files and custom names for the compiled files.