Naming is a complicated cognitive process, which consists of different stages. In psycholinguistics, cognitive psychology, cognitive neuropsychology and neurolinguistics it is one of the most debated issue in terms of the actualization the name after perceiving the object. The study of naming process has a great importance, because without analyzing normal cognitive functioning could not be explained the age - and damage - related changes of higher psychic functions. The development of modern approaches and models were based on the classic aphasiology. Over time contradictory data and facts have been gathered to be analyzed. In most cases, this situation requires the revision of existing viewpoints, which in turn develops revised or new cognitive models. In this article we discuss changing patterns of viewpoints about cognitive processes underlying naming and modern cognitive models of naming: anatomical, multiple semantic, logogen-pictogen and connectionistic. In this publication we describe modern models, which exist simultaneously. None of them could fully explain the naming process. This is because of complexity of the naming; the adequate approach is selection of appropriate model framework for different aspect sand components of the naming.