Background: The renaming of program identifiers is the most common refactoring operation. Because some identifiers are related to each other, developers may need to rename related identifiers together. Aims: To accurately recommend identifiers that should be renamed together, it is necessary to consider the relationships between identifiers in the program and the brief matching for non-identical but semantically similar identifiers. Method: In this study, we investigate the relationships between co-renamed identifiers and identify the types of relationships that contribute improving the recommendation using more than 1M of renaming instances collected from the histories of open source software projects. We also evaluate and compare the impact of co-renaming and the relationships between identifiers when inflections occur in the words in identifiers are taken into account. Results: As a result, we revealed several relationships of identifiers that frequently found in the co-renamed identifiers, such as the identifiers of methods in the same class or an identifier defining a variable and another used for initializing the variable, depending on the type of the renamed identifiers. Additionally, the consideration of inflections did not affect the tendency of the relationships. Conclusion: These results suggest an approach that prioritize the identifiers to be recommended depending on their types and the type of the renamed identifier.