While LLMs enable personalized chatbots, their effectiveness in child-centered personalization remains unclear, as systematic evaluation of child-specific preferences is still lacking. To address this gap, we introduce ChildEval, a benchmark for evaluating LLMs' ability to infer and follow child-centered preferences in long-context conversations. ChildEval contains 29K synthesized persona profiles of children aged 3-6, providing relatively static background information. Each persona is associated with a child preference-which may align with, conflict with, or be independent of the persona-expressed either explicitly in a single sentence or implicitly through 6-10 turn dialogues. Explicit and implicit preferences are designed to reflect the same underlying preference but differ in expression, capturing dynamic aspects of preference expression rather than changes in the static persona. The benchmark spans five top-level and fourteen sub-level categories covering children's daily lives and development. We further propose fine-grained, child-centric evaluation protocols to systematically assess open-source LLMs. Experimental results demonstrate how different personalized representations affect LLM responses and suggest that finetuning on ChildEval can enhance child-centered performance. Our code and dataset are available at https://github.com/ziyanluo/ChildEval.