No, you do not need to have a specific, named condition in order to be put into the Support Group. However, DWP decision makers do have access to a list of conditions and what can be expected from those. I suppose it might be easier for them to accept a claim if they can turn to this and see that the claimant's reported limitations correlate to this.
The PDF version of the form is here, if you want to have a look at the changes
Using The PDF Version Of The ESA50 Questionnaire