The phrase "several different names" means that there are multiple distinct and unique identifiers or labels for a particular person, place, thing, or idea. Full definition
This service has been around for awhile, though under several different names. (lincolncole.net)
This name is said to derive from several different names in history. (babygaga.com)
There are loads of different cloth diaper brands and styles, several different names for the exact same products and there can be conflicting information everywhere you turn. (clothdiapergeek.com)