I don't think there is any way to closely translate the Persian and have it make any sense, much less have a double meaning.

It all rests on "jushe shirin" which is "sodium bicarbonate" in English and "jush zadan". I have researched my thesaurus for possible English synonyms for "jush zadan" that might possibly sound like a woman's name. No luck.

But we can find some puns related to the baker's business. The one I suggest can be read as the baker needs his money (dough) and can also be read as the baker kneads his dough.

I have no idea what your context is, but maybe the suggestion will be useful.

Well, it's so hard to convey all there is in this cute play of words into English; however, since frizz means both the bubbling act caused by baking soda as well as worrying about one's dearest, I think this translation could convey the most out of the original.

i think it depends on the context. if it is talking about people who are not doing their job as their supposed to do( with jusheh shirin here), the sentence must be translated in a different way, if not using dough is a great idea.

as long as this phrase is an amphibology,anyone with different comprehension may translate sth different.
here the thought of baker worriation for shirin rang a bell in my mind and what i wrote above can have two different meaning"نانوا نیز نگران شیرین است" و"نانوا نیز خواستار شیرین است"