Short answer. No, not by itself. The Civil Code states that the continued use of the partnership name, or of a deceased partner's name as part of it, shall not of itself make the individual property of the deceased partner liable for debts contracted by the continuing business.
What the law says
The use by the person or partnership continuing the business of the partnership name, or the name of a deceased partner as part thereof, shall not of itself make the individual property of the deceased partner liable for any debts contracted by such person or partnership.
Civil Code, Article 1840 — Creditors When the Business Continues. Read the full provision →
The article says so in terms
This is the closing sentence of the article, and it is directed at precisely the worry you have. The use by the person or partnership continuing the business of the partnership name, or the name of a deceased partner as part of it, shall not of itself make the individual property of the deceased partner liable for any debts contracted by that person or partnership. Continuing to trade under the familiar name is not, by itself, an act that binds the estate.
The weight carried by not of itself
Those three words define the limit of the protection. The rule addresses one specific inference — name, therefore liability — and rejects it. It does not say the estate can never be liable for anything. Liability arising from some other source is untouched: an undertaking actually given, an interest in the business that remains and is drawn upon, or an obligation the deceased incurred in their lifetime. What the sentence removes is liability inferred from the signage alone.
Why a rule like this is needed
The name of a professional or trading firm is often its most valuable asset, built over decades and frequently carrying the name of someone who has died. Without this sentence, every continuing firm would face a choice between abandoning its identity and exposing a deceased partner's estate to obligations contracted long after their death. The article lets the name continue as a name.
What the estate should still watch
Two things in the same article are worth attention. Creditors of the dissolved partnership become creditors of the continuing business in the listed situations, which is a different question from new debts. And the article gives those creditors a prior right, as against the separate creditors of the deceased partner's representative, to any claim of the representative against the continuing business on account of the deceased partner's interest in the dissolved partnership.
What the estate's representative should still do
The protection is against an inference, so the practical task is to make sure no other basis for liability is quietly created. Check whether the representative has signed anything on the continuing business's behalf, whether the deceased's interest in the old partnership has in fact been settled, and on what terms. Where the interest remains outstanding, remember that the article gives the dissolved partnership's creditors a prior right to any claim the representative has against the continuing business on account of that interest.