Sentence 2 is the better sentence; even though there will be several
signatures from the government, each company is applying for only one
You could also say, to be perfectly clear:
A/ Any/ Each/ Every company doing e-commerce should apply for
an/ its electronic signature from the government.
Or, to focus on the plural, you could say:
Companies doing e-commerce should apply for their electronic
signatures from the government.
Adding the possessive adjective their to sentence
(b) clarifies it.
These sentences could also be arranged with the phrase to the
government coming right after apply.
A company doing e-commerce should apply to the government for an
Companies doing e-commerce should apply to the government for their