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Article - CS36889 - How to specify a feature name as a parameter in Pro/ENGINEER, Creo Elements/Pro and Creo Parametric? (ptc.com)
If you would elaborate on the design intent motivating this desire to use the group name, it may spur some alternative options to manage what you require. My example above would support driving a dimension from the group via a feature parameter of the group.
To follow what I did you need to consider the levels of parameters available for use in Creo. Considering that if you are in part mode; parameters can be assigned to sections, features, and parts. There are more types of parameters (system and others) but consider part mode to start with. It can quickly become a convoluted mess if you are not quite deliberate about mapping out design intent and structuring the models to support the intent.
Groups are a feature type in Creo and feature parameters can be mapped to a group. The group has a feature ID (meaning Creo treats the group as a feature) as shown in my first screenshot above.
Overview of parameter terms:
Terminology Used in Relations and Parameters (ptc.com)