In English, when we want to express what someone or something is, we can use the form of "itis" or "its". For example, we can say "Itisacat" or "Itsacat". These two expressions have the same meaning, both of which mean a cat. In the name "ItsAmy", "its" is used to represent the abbreviation of "itis", which means "this is Amy". So "ItsAmy" means "this is Amy".
It should be noted that in formal English writing, abbreviations are usually not used, but are expressed in complete sentences. For example, in formal writing, we may write "ItsAmy" instead of "it Sammy". But in oral and informal writing, abbreviations are very common.