When in doubt, break your sentence apart so the subject and verb in question go together, like so:
- Explorer James Cook (give?) New South Wales its name.
Use the third person past tense. James Cook only named New South Wales once, and he did it in the past. The process of naming it was also quantifiable (in this sense instantaneous). Explorer James Cook gave New South Wales its name.
You would use present perfect if you were trying to say that James Cook just very recently gave New South Wales its name. Present perfect takes a form like this:
- Explorer James Cook has given New South Wales its name.
Can you tell from phrasing it this way that the present perfect isn't the right form?