There are two countries named after the Equator.
One is Ecuador. The Equator passes right through Ecuador, just a little bit north of the capital, Quito. Very good.
The other is The Republic of Equatorial Guinea. The southern border of Equatorial Guinea follows the 1° parallel, and the southernmost point in Equatorial Guinea is the Isla de Corisco, at a latitude of 0°55”2” north. The equator does not pass through any point of Equatorial Guinea.
If I were in charge of naming a country, I think I would have done better than this.