Step 1: Understand the structure of the compound.
The given compound is CH$_3$COOC$_2$H$_5$, which is an ester formed by the reaction of acetic acid (CH$_3$COOH) and ethanol (C$_2$H$_5$OH).
Step 2: Analyze the options.
- Methyl propanoate (Option A) is incorrect because the ester is formed from acetic acid and ethanol.
- Ethyl ethanoate (Option B) is the correct IUPAC name for CH$_3$COOC$_2$H$_5$, where "ethyl" comes from the ethanol part and "ethanoate" refers to the acetic acid part.
- Acetotheane (Option C) is not a valid name.
- Ethoxyethane (Option D) refers to an ether, not an ester.
Step 3: Apply to the options.
The correct IUPAC name is (B) Ethyl ethanoate.
Final Answer:
\[
\boxed{\text{Ethyl ethanoate}}
\]