This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F439 offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “hamster” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: face, pet.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: 🐹︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
Hamsters are rodents (order Rodentia) belonging to the subfamily Cricetinae, which contains 19 species classified in seven genera. They have become established as popular small pets. The best-known species of hamster is the golden or Syrian hamster (Mesocricetus auratus), which is the type most commonly kept as a pet. Other hamster species commonly kept as pets are the three species of dwarf hamster, Campbell's dwarf hamster (Phodopus campbelli), the winter white dwarf hamster (Phodopus sungorus) and the Roborovski hamster (Phodopus roborovskii).
Hamsters are more crepuscular than nocturnal and, in the wild, remain underground during the day to avoid being caught by predators. They feed primarily on seeds, fruits, and vegetation, and will occasionally eat burrowing insects. Physically, they are stout-bodied with distinguishing features that include elongated cheek pouches extending to their shoulders, which they use to carry food back to their burrows, as well as a short tail and fur-covered feet.