I’m thinking of a city with 7 letters in its name. The first 4 letters are shared with a certain kind of bird. The 4th and 7th letters are the same. It is NOT the largest city in its country. What's the answer?

The answer is Hagåtña.

Explanation:

The only city that matches these descriptions is Hagåtña.  It is one of Guam's capital cities.  Guam is a tiny western Pacific island and a U.S. territory for more than a century now.  "Haga” was the name of an eagle family often depicted with two heads.  It was a rare kind of bird in the eagle family.  Hagåtña is a seven-letter city name.  The first 4 letters are shared with this ancient bird called "Haga."  The 4th and 7th letters are the same, as you can see from the spelling of Hagåtña.

"facing the rising sun of our new day begun

let us march on till victory is won.",

because the rising sun is a symbol of hope.