The most common name for a point of land extending into a body of water is peninsula. Usually a peninsula has water around three of its sides. The Yucatan Peninsula is an example of a peninsula.
Other words that may mean the same are cape, headland, point, and spit. A cape is usually a large point of land that goes into the sea. A headland juts into a bay and has high cliffs. A spit is a sandy point of land extending into a body of water from a beach.
A small body of land surrounded by water would be an island and very large ones would be called continents.
Island body of land with water around it
Island body of land with water around it
There appears to be a word left out of the question. Assuming this word is "water" ("What is the name given to a body of land with water surrounding it?"), the answer is "island".
The name is an island.
island
an island
a island
It is an island.
name given to point of land extending into a body of water
a fresh water pond
an island
a fresh water pond