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I want to name the specific client on my resume. Our firm is on the public docket for the client, but I'm not, since I'm fairly junior. I'm not going to put a separate matter section, just say "Represented Big Name Co., Inc. by.." rather than "Represented a large company by.." under the experience section for my firm.

Is this okay to do?

Do not do this. You can talk about what you did on the matter and that it was a large company, but outright stating who the client is would be a major red flag. I'd avoid saying anything that would allow people to infer the client's identity as well.

edit: If you want to see how to do this pull up some firm profiles and look at how they handle it.

No, not unless you were seconded (outplaced by your firm) to that client for a year or two. And, if so, make it clear who your employer was during that time. And, if the post below is correct, okay it with the client to which you were seconded for a significant period of time. Otherwise, in Atlanta, for example, all firms understand which company you mean when listing "a major soft drink company".

I think it's an ethics violation in most states to disclose a client's name without their consent.

OP here:

I spoke with some people who have left my firm and they said I could put the name without concern. Also this is litigation where the firm's representation is fully public. I'll change the wording, but just throwing some thoughts out there.

I would not put any client company name on a resume without their prior consent. However, law firms reveal their client list frequently, but that is different than on one's resume.
I read several expert witness CVs that listed the type of client by industry & size, but not by name. Of course, that would be revealed when checking for conflicts, but not on one's CV or resume.
Nevertheless, practices can differ by region or by firm.