The functions are the smallest naming unit of aggregation behavior in most traditional programming languages. The readability of function names plays a vital role in programmers’ understanding of program functions and the interaction between different modules. Low-quality function names may confuse developers, increase the smell in the code, and then result in software defects caused by API misuse. Therefore, a method of function name consistency checking and recommendation based on deep learning is proposed, which is named DMName. Firstly, for the given source code of the target function, the internal context, interactive context, sibling context, and closed context are constructed respectively, and the context information tag sequence is obtained after merging them. Then the tag sequence is converted into the context representation vector sequence by using the word embedding technology FastText and input into the encoder of the seq2seq model. The copy mechanism and coverage mechanism are utilized to solve the OOV problem and the repeated decoding problem, respectively. Finally, the vector sequence of the prediction result of the target function name is output, and the consistency of the function name is predicted with the help of the two-channel CNN classifier. If the function name is inconsistent, the recommended function name can be obtained by direct mapping according to the vector space similarity matching. The experimental results show that the F1-measure of DMName in function name consistency check and recommendation reaches 82.65% and 73.31% respectively, which is 2.01% and 2.96% higher than the current optimal DeepName. Finally, the DMName is verified in the large-scale open-source project, namely lancia in GitHub. A total of 16 function name inconsistency problems are found, and reasonable name recommendations are made, which further confirms the effectiveness of DMName.