The DICOM standard has rather more to say about names than that:
A character string encoded using a 5 component convention. The character code 5CH (the BACKSLASH "\" in ISO-IR 6) shall not be present, as it is used as the delimiter between values in multiple valued data elements. The string may be padded with trailing spaces. For human use, the five components in their order of occurrence are: family name complex, given name complex, middle name, name prefix, name suffix.
Any of the five components may be an empty string. The component delimiter shall be the caret "^" character (5EH). Delimiters are required for interior null components. Trailing null components and their delimiters may be omitted. Multiple entries are permitted in each component and are encoded as natural text strings, in the format preferred by the named person.
For veterinary use, the first two of the five components in their order of occurrence are: responsible party family name or responsible organization name, patient name. The remaining components are not used and shall not be present.
This group of five components is referred to as a Person Name component group.
For the purpose of writing names in ideographic characters and in phonetic characters, up to 3 groups of components (see Annexes H, I and J) may be used. The delimiter for component groups shall be the equals character "=" (3DH). The three component groups of components in their order of occurrence are: an alphabetic representation, an ideographic representation, and a phonetic representation.
Any component group may be absent, including the first component group. In this case, the person name may start with one or more "=" delimiters. Delimiters are required for interior null component groups. Trailing null component groups and their delimiters may be omitted.
Precise semantics are defined for each component group. See Section 6.2.1.2.
For examples and notes, see Section 6.2.1.1.