That object is a teapot. While the compound noun "water container" makes sense, it isn't really accepted, so if you say "water container" it will seem as if you're inventing the compound noun. I am guessing that you may be referring to the kettle, which is the container one fills with water and then sets on the stove to boil (once the water is boiling, one pours it over tea leaves or teabags in the teapot to steep or brew and then serve).
Here's a bonus. Both "teapot" and "kettle" have a place in English proverbs or terms of art. "A tempest in a teapot" means a lot of drama with no great significance. (A "tempest" is a huge storm, but a teapot is a small, domestic object.) And "kettle" appears in the wonderful expression "the pot calling the kettle black," which is akin to "people who live in glass houses shouldn't throw stones." If I have had too much alcohol to drink the last three nights, and then on the fourth scold my friend for getting tipsy at dinner, he might tell me "This is the pot calling the kettle black!" The pot and the kettle are both black, so it's hardly fair for me to be scolding my friend for "misbehavior" I've just exhibited myself. In Black American English, this expression is sometimes altered to: "Hello, kettle? This is pot. You're black!"