Embedding models have demonstrated strong performance in tasks like clustering, retrieval, and feature extraction while offering computational advantages over generative models and cross-encoders. Benchmarks such as MTEB have shown that text embeddings from large language models (LLMs) capture rich semantic information, but their ability to reflect code-level functional semantics remains unclear. Existing studies largely focus on code clone detection, which emphasizes syntactic similarity and overlooks functional understanding. In this paper, we focus on the functional consistency of LLM code embeddings, which determines if two code snippets perform the same function regardless of syntactic differences. We propose a novel data synthesis framework called Functionality-Oriented Code Self-Evolution to construct diverse and challenging benchmarks. Specifically, we define code examples across four semantic and syntactic categories and find that existing datasets predominantly capture syntactic properties. Our framework generates four unique variations from a single code instance, providing a broader spectrum of code examples that better reflect functional differences. Extensive experiments on three downstream tasks-code clone detection, code functional consistency identification, and code retrieval-demonstrate that embedding models significantly improve their performance when trained on our evolved datasets. These results highlight the effectiveness and generalization of our data synthesis framework, advancing the functional understanding of code.