Projects, Time spent reporting

Projects, Time spent reporting

The workaround I use to report on time spent on projects is to create a custome field in the Request template that I simply call "Project name".
In this field i copy -> paste the project name. Now I can create a custom time-spent report and use this custom field as an identifyer for this project.
Why "project" isn't available by default in time-spent reporting is a mystery to me, but that's how it is.
Needles to say, I've assosiated this request to the actual project.

My question: Is there a way for me to auto populate my custom "project name" field ? Say with some variable name that points to the actuall project name ?

Something like in the attached image.

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