Naming a coordination compound
Yes, you are correct: an -ate prefix is used when the complex has a net negative charge and the name should be triamminetrinitritocobaltate(I) ion

Reference:


  If the overall coordination complex is an anion, the ending "-ate" is attached to the metal center. Some metals also change to their Latin names in this situation. The rest of the metals simply have -ate added to the end (cobaltate, nickelate, zincate, osmate, cadmate, platinate, mercurate, etc. Note that the -ate tends to replace -um or -ium, if present).


Chemistry Libretexts - Nomenclature of Coordination compounds