Following your logic Lake Michigan should be renamed Lake America. There’s a bunch of lakes up there, do they all get renamed Lake of America? Seems confusing!

Here’s a list of all the gulfs in the Americas:

North America

1. Gulf of Mexico
2. Gulf of Alaska
3. Gulf of California (Sea of Cortes)
4. Gulf of St. Lawrence
5. Gulf of Honduras
6. Gulf of Panama
7. Gulf of Tehuantepec

Central and South America

8. Gulf of Darien (Colombia and Panama)
9. Gulf of Venezuela
10. Gulf of Guayaquil (Ecuador)

Following your logic, they’re all badly named because that’s just named after the region they’re in, not the content.