“The given name Eric, Erik, or Erick is derived from the Old Norse name Eiríkr (or Eríkr in Eastern Scandinavia due to monophthongization). The first element, ei- is derived either from the older Proto-Norse *aina, meaning “one, alone, unique”, as in the form Æinrikr explicitly, or from *aiwa “long time, eternity”. The second element -ríkr stems either from *ríks “king, ruler” (cf. Gothic reiks) or from the therefrom derived *ríkijaz “kingly, powerful, rich”. The name is thus usually taken to mean “sole ruler, autocrat” or “eternal ruler, ever powerful.”

There are seven theories for the name Roth:

• the spilling of blood from the warrior class of ancient Germanic Deutsch soldier
• ethnic name for an Anglo-Saxon, derived from rot (meaning “red” in pre-7th century), referencing red-haired people
• topographical name, derived from rod (meaning “wood”), referencing a dweller in such a location
• derivative from hroth (from the Proto-Germanic word for “fame”; related to hrod)
• locale name for 18th century Ashkenazi refugees to Germany
• derivative from roe (king) in the ancient Danish language
• of the red colour of clay, as in pottery (Deutsch)

Source: Wikipedia