Pandas/Python create columns based on multiple conditions with a dictionary

I am looking for a shorter and more elegant way of writing the condition below, let's say I have 30 different combinations. Is it possible to map some kind of dictionary with multiple conditions or something else?

def set_name(df):
    if df['PRODUCT'] == 'A' and df['TYPE'] == 'C2':
        return 'AAC2'
    elif df['PRODUCT'] == 'A' and df['TYPE'] == 'C3':
        return 'AAC3'
    elif df['PRODUCT'] == 'B' and df['TYPE'] == 'C2':
        return 'BBC"'
    
df['RETURN'] = df.apply(set_name, axis=1)

Another way is the below which still pretty long if I have many combinations.

conditions = [
    (df['PRODUCT'] == 'A') & (df['TYPE'] == 'C2'),
    (df['PRODUCT'] == 'A') & (df['TYPE'] == 'C3')
]

values = ['AAC2', 'AAC3']

df['RETURN'] = np.select(conditions, values)