How did Worcester get its name?

The Worcester Tornadoes are named after the F4 tornado that devastated Worcester, Massachusetts on June 9, 1953.

Usually Jim or Jimmy is short for James

"your name is" is correct English and when used in this way means both your full name or a part of your name (usually surname, depending on the context). "your names are" is also correct English, but...

It is the name of its genus.

binominal nomenclature, binary nomenclature, or binomial classification system. so yes