Targeting different frameworks but have one Nuget Package

Is it possible at all?  I am trying to figure out the best way to go about this.

We have a project, say the project is named "DoFunkyStuff".

We want to have two versions of this project, one that is build on .Net Core, and one that is built on the Full .net 4.5.6 Framework.

Firstly, how would I go about structuring these projects in my solution, so that I could have both of these built into one Nuget package, that is structured targeting the different frameworks.

Is this possible without having different project names?

Any guidance would be amazing.