Identify the name carefully

Aspartame is given as aspartyl phenylalanine methyl ester.

This means:

• It is a dipeptide made from aspartic acid and phenylalanine.
• The suffix methyl ester means the terminal carboxylic acid group is present as $-COOCH_3$

Interpret “aspartyl phenylalanine”

The word aspartyl means the residue from aspartic acid forms the N-terminal part of the peptide.

So the sequence is: $\text{Aspartic acid} - \text{Phenylalanine}$

Write the relevant side chains

• Aspartic acid side chain: $-CH_2COOH$
• Phenylalanine side chain: $-CH_2C_6H_5$

Form the peptide linkage

In a dipeptide, the peptide bond is: $-CO-NH-$

Therefore the skeleton must be: $NH_2-CH(CH_2COOH)-CO-NH-CH(CH_2C_6H_5)-COOCH_3$

Key structural features to check in the options

The correct structure must contain all of the following:

1. Free amino group at the aspartyl end: $NH_2-CH(\cdots)$
2. Aspartic acid side chain: $-CH_2COOH$
3. Peptide bond: $-CO-NH-$
4. Phenylalanine side chain: $-CH_2C_6H_5$
5. Terminal methyl ester: $-COOCH_3$

Match with the given options

Among the given choices, the structure corresponding to $NH_2-CH(CH_2COOH)-CO-NH-CH(CH_2C_6H_5)-COOCH_3$ is Option B.

Final answer

Therefore, the correct option is: $\boxed{B}$