In both English and Chinese cultures, a person has 3 names: a surname and 2 given names. Surnames (family names) are usually copies of the father's name. The wife (in the US) and children all use that surname.
In Chinese culture, given names can be any two Chinese words. In the US, a given name is (usually) not an English word. This is easy in English, since most given names (and most words) are 2-4 syllables long.
In US culture, about 80% of given names are standard names, not new words. There are thousands of standard names. Each one has various spellings and nicknames. For example the name "Katherine" can be Kathy, Kate, Kat, Catherine, Cathy, Cate, Caty, or even Catlyn. So one "traditional" name creates 9 modern names.
What is the basis for creating a new English name word?
There is no rule. There is no law. In theory, it can be anything.
Sometimes it is a nickname (like "Bubba"). Sometimes it is a name from a foreign country (like "Monique" from France). Sometimes a surname is used as a given name ("Cooper", "Morgan"). Sometimes the name reflects a subculture. Many Afro-American names are created using popular endings (like "-isha", "-iqua").
But it can be anything the parents choose. Once a child is a teen-ager or adult, they can choose to "be called" something else, if they don't like their official name. They might use a nickname, or initial letters, etc.