I have an earlier answer about how so many colonialist cities got the "New" name, and why it was an honor. As you can probably guess, the story involves money.

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I wouldn't want to throw a uniform blanket over colonial naming practices in America and Australia, of course. But one important factor to consider in many cases where something is named "in honor of" a person or an Old World place is: who's paying? This can mean directly, in terms of financing, or indirectly, in terms of political support to secure a charter and influence financing decisions.

A good illustrative example of this phenomenon is Plymouth, because the Pilgrims did not come from Plymouth except on a technicality (Plymouth in Devon was a key port for sailing to the Americas).

In the early 17th century, England chartered two trade companies to settle "Virginia" (the eastern seaboard of the present-day US): the London Company for the mid-ish region and the Plymouth Company for the north-ish. The two were named for the base of operations of their major financial backers, particularly Thomas Smith (or Smythe) in London and Ferdinando Gorges in Plymouth.

The Plymouth Company's first attempt at a colony, in Maine, was initially named Popham Colony after its major financial backer, John Popham. The Plymouth settled by the Pilgrims in 1620 was thus the second attempt at a colony, this time named for its funding company/the base of operations of the company's most important backers.

Acknowledging financial and political supporters by name or location pops up in various ways. 16th century maps show that Giovanni da Verrazzano made an aborted attempt to name the waters around New York City "Angoulesme" or "Angouleme" after his patron, King Francis I--a.k.a. the Count of Angouleme. Sydney in Nova Scotia (Canada) and Australia were both named for Thomas Townshend, Baron Sydney, by their early governors for his political support in expeditions to Canada and Australia--and in choosing who would be governor. Sydney is a useful example, I think, because it shows the flexibility of name, title, geographic affiliation in bestowing a tributary name. For example, New York is pretty directly (re)named as such because its proprietor was the Duke of York in England (a.k.a. James II; Albany takes its name from his Scottish title as Duke of Albany).

And sometimes the association was present without being a direct copy--Jamestown, of course, but you might also be interested in /u/imaginarystudy's excellent (far better than mine here) response about the origins of the name "Virginia."

Further Reading:

• D.W. Meinig's The Shaping of America, Vol. 1: Atlantic America feels a bit like using a nuclear bomb to kill a flea in this case, but if you're also looking for a more history-filled introduction to historical geography, it might be worth it--I think Meinig's approach holds some interesting lessons for the current move towards incorporating environmental factors into historical causation and narratives.