Federated learning (FL) is a type of collaborative machine learning where participating peers/clients process their data locally, sharing only updates to the collaborative model. This enables to build privacy-aware distributed machine learning models, among others. The goal is the optimization of a statistical model's parameters by minimizing a cost function of a collection of datasets which are stored locally by a set of clients. This process exposes the clients to two issues: leakage of private information and lack of personalization of the model. On the other hand, with the recent advancements in various techniques to analyze data, there is a surge of concern for the privacy violation of the participating clients. To mitigate this, differential privacy and its variants serve as a standard for providing formal privacy guarantees. Often the clients represent very heterogeneous communities and hold data which are very diverse. Therefore, aligned with the recent focus of the FL community to build a framework of personalized models for the users representing their diversity, it is also of utmost importance to protect the clients' sensitive and personal information against potential threats. To address this goal we consider $d$-privacy, also known as metric privacy, which is a variant of local differential privacy, using a a metric-based obfuscation technique that preserves the topological distribution of the original data. To cope with the issue of protecting the privacy of the clients and allowing for personalized model training to enhance the fairness and utility of the system, we propose a method to provide group privacy guarantees exploiting some key properties of $d$-privacy which enables personalized models under the framework of FL. We provide theoretical justifications to the applicability and experimental validation on real datasets to illustrate the working of our method.