Multimodal Large Language Model (MLLM) Personalization is a critical research problem that facilitates personalized dialogues with MLLMs targeting specific entities (known as personalized concepts). However, existing methods and benchmarks focus on the simple, context-agnostic visual identification and textual replacement of the personalized concept (e.g., "A yellow puppy" -> "Your puppy Mochi"), overlooking the ability to support long-context conversations. An ideal personalized MLLM assistant is capable of engaging in long-context dialogues with humans and continually improving its experience quality by learning from past dialogue histories. To bridge this gap, we propose LCMP, the first Long-Context MLLM Personalization evaluation benchmark. LCMP assesses the capability of MLLMs in perceiving variations of personalized concepts and generating contextually appropriate personalized responses that reflect these variations. As a strong baseline for LCMP, we introduce a novel training-free and state-aware framework TAME. TAME endows MLLMs with double memories to manage the temporal and persistent variations of each personalized concept in a differentiated manner. In addition, TAME incorporates a new training-free Retrieve-then-Align Augmented Generation (RA2G) paradigm. RA2G introduces an alignment step to extract the contextually fitted information from the multi-memory retrieved knowledge to the current questions, enabling better interactions for complex real-world user queries. Experiments on LCMP demonstrate that TAME achieves the best performance, showcasing remarkable and evolving interaction experiences in long-context scenarios.