Short answer. Yes. The rule against a limited partner's surname appearing in the firm name has an exception exactly for you: it does not apply where, prior to the time when the limited partner became such, the business has been carried on under a name in which his surname appeared.
What the law says
Prior to the time when the limited partner became such, the business has been carried on under a name in which his surname appeared
Civil Code, Article 1846 — Surname of a Limited Partner. Read the full provision →
The general rule and why it exists
The default rule is that the surname of a limited partner shall not appear in the partnership name. That rule protects creditors, who might otherwise assume anyone named in the firm's name is a general partner with unlimited personal liability. Letting a limited partner's surname sit in the firm name without qualification risks misleading people the partnership deals with about who actually stands behind its debts, since a limited partner's own liability is capped at what was contributed, unlike a general partner's.
Your situation fits the second named exception
The rule carves out two exceptions. The first is where the surname is also that of a general partner. The second — the one that matches your facts — applies where the business was already carried on under a name in which his surname appeared before you became a limited partner. Since your surname clearly predates your becoming a limited partner, this exception covers your situation directly.
What happens if the exceptions do not apply
When neither exception applies and a limited partner's surname appears in the firm name anyway, the consequence is serious: that partner is liable as a general partner to partnership creditors who extend credit to the partnership without actual knowledge that he is not a general partner. That is the exposure the exception is specifically protecting you from — full general-partner liability toward whichever creditors reasonably relied on the firm name in deciding to extend credit. The consequence binds only creditors who actually lacked knowledge; one who already knew you were merely a limited partner cannot invoke it.
Why the exception protects you specifically
The exception exists because the name in this situation did not create a false impression when your surname first appeared in it — the business already used that name before you had any partnership stake in it at all. Creditors dealing with the firm under its longstanding, established name are not being genuinely misled about your actual status by a surname that was already there long before your limited partnership interest even began to exist.