You can, mechanically — but doing it hands that client's personal information to the company behind the tool, and that has to clear the same bar any other disclosure does.
Short answer
Mechanically, yes. Legally, the moment a client's name leaves your system and enters a public AI tool, it has become information “in the possession or custody” of a third party, and your business is still accountable for it. A name attached to any other detail about that person is personal information under Canadian privacy law without needing anything more identifying than that — and the safer default is to ask whether the name was actually necessary for what you're asking the tool to do.
This is a narrower, more common scenario than deliberately feeding a model bulk customer records to train or fine-tune it — see the separate question of training a model on customer records for that version. Pasting one client's name into a public chatbot while drafting an email or summarizing a file is still a transfer of that information to a third party. PIPEDA Schedule 1, clause 4.1.3 treats a transfer for processing as something your business remains accountable for — it doesn't distinguish between a bulk upload and a single line typed into a chat window.
Under PIPEDA, personal information is defined broadly as information about an identifiable individual — a client's name, on its own or paired with almost any other detail in the same prompt (a file number, an address, a dollar figure, a date), is squarely inside that definition. Canada's joint privacy-commissioner generative-AI principles give the practical response directly: organizations should “use anonymized, synthetic, or de-identified data rather than personal information where the latter is not required to fulfil the identified appropriate purpose(s).” If the task works just as well with “the client” or a file number instead of a real name, that's the version to paste.
Whether this is a real problem for your business or a low-stakes one depends heavily on which product and which tier you're actually using — a consumer chatbot's default terms behave very differently from an enterprise or API tier with contractual data-use limits. The service-provider question covers how to tell which one you're on. Until you've checked, the safest default is to de-identify first and paste the client's real name only on a tier your business has actually reviewed.
See how a live AI system gets kept accountable once it's running.