In programming, the names for the program entities, especially for the methods, are the intuitive characteristic for understanding the functionality of the code. To ensure the readability and maintainability of the programs, method names should be named properly. Specifically, the names should be meaningful and consistent with other names used in related contexts in their codebase. In recent years, many automated approaches are proposed to suggest correct names for methods, among which neural machine translation (NMT) based models are widely used and have achieved state-of-the-art results. However, these NMT-based models mainly focus on extracting the code-specific features from the method body, in which the global features, including the project-specific context and documentation of the target method, are ignored. We conduct a statistical analysis to explore the relationship between the method names and their contexts. Based on the statistical results, we propose GTNM, a Global Transformer-based Neural Model for method name suggestion, which considers the local context, the project-specific context, and the documentation of the method simultaneously. Experimental results on java methods show that our model can outperform the state-of-the-art results by a large margin on method name suggestion, demonstrating the effectiveness of our proposed model.