Privacy is becoming a pressing requirement that spawns across different network layers and user interactions. Using multiple identifiers for the same user, pseudonyms, as means for preserving privacy, is becoming an important approach that has not seen proper discussion or validation. This paper presents formalization on pseudonymity specially considering its influence on the network stack. It presents a study on privacy requirements and its implementation cost, both at theoretical and practical levels, through the support of multiple network stack instantiations and network identifiers per user. We discuss how pseudonyms can be used to preserve users' privacy, and what key issues and requirements are needed, to use, control, and evaluate a pseudonym-based solution at network level. The paper further presents an architecture that builds a pseudonym-based solution supported throughout the network stack, describes its implementation in a real testbed, and depicts the results obtained related to both efficiency and costs of such a privacy approach. Finally, it discusses the characteristics of the architecture according to the identified privacy requirements, its impacts and constraints.