The name of the gulf located east of Texas west of Florida and north of southern Mexico is The Gulf of Mexico
The Gulf of Mexico.
There is no Gulf possible between the regions as you state them - Mexico is to the west of Florida and therefor there can not be a Gulf WEST of Florida AND north and southern Mexico. Your question makes no sense and thus can not be answered.
The Gulf of Mexico
No, in North America bees have only reached Mexico and some of the southern states of the US (Texas, Florida, New Mexico etc.)
Arizona new Mexico Texas Mississippi Alabama Louisiana georga south Carolina Tennessee
Gulf of Mexico
Florida is slightly closer, as its southernmost city, Key West, is near 24.56° North latitude. For Texas, the southernmost point is South Point, near Brownsville, at 25.87 North latitude.
The Chihuahuan Desert enters far west Texas, much of southern New Mexico, southeastern Arizona and central Mexico all the way to Zacatecas.
The Musk turtle can be found from southern Ontario, southern Quebec, and Southern Maine to the north, south Florida, and East central Texas. Other places where they live are central Wisconsin and Minnesota.
The jaguar, found in Mexico, and small isolated populations in southern parts of Texas, Arizona, and New Mexico.
From the geograhic center of Texas that is Oklahoma however from certain locations in West Texas it would be New Mexico.