What is this idiom: "I'm going to start taking names and..."?

There is some idiom that starts out like,

"I'm going to start taking names and..." I can't remember the rest of it. What is it and when is it used?

Are you perhaps referring to this?

I'm going to start kicking ass and taking names

Kicking posteriors and taking names

The expression "kicking butt/ass and taking names" may go back as far as World War II, although the earliest cited source in J.E. Lighter, Random House Historical Dictionary of American Slang (1997) is from 1962. Here is the relevant part of Lighter's entry:

kick ass {or (euphem[istically]} butt or tail} 1. Esp. Mil[itary] to enforce one's authority or otherwise enforce oneself mercilessly or pugnaciously; (also) (prob. the orig. sense) to subdue others by beatings; (hence) to play the bully; in phr. kick ass and take names to do so with great determination or success.—also used fig.—usu. considered vulgar.

The two earliest citations in Lighter are

1962 Killens Heard the Thunder 44 {ref. to WWII} Them Japs are kicking asses and taking names [in the Pacific].

and

1968 Mares Marine Machine 29: The juniors take the role of bad guys, "kicking ass and taking names," in DI [Drill Instructor] parlance.

Somewhat surprisingly, Google Books search results don't record a match for any version of this phrase until 1975 and 1976, when two instances occur. From U.S. Department of the Army, Soldiers, volume 30 (1975) [combined snippets]:

Lessons Learned. Later, the lanky ex-Marine says of IMA [Institute for Military Assistance], "When I first got out here I didn't know what Civil Affairs or Psychological Operations was. I just had to sit back and say to these guys, 'Tell me what you can do for me.' And they've really taught me a lot."

Charlie Company commander. Captain Louis Curl, expresses what he learned more bluntly: "You can't go into an area, kick ass and take names. In a guerrilla situation you can't get anywhere without the support of the people. And I've gotten that support through my Psyops and CA people."

And from U.S. Federal Railroad Administration, Proceedings of the 1976 Conference: Employee Assistance Programs: An Alternative to Tragedy

Basically, [our supervisors are] very short in understanding their responsibilities and the procedures that are available to them to handle people problems. So, by going through the system with management seminars and talking to supervisors, we've been able to upgrade their ability to work with people. That is the weakest link that I've detected in our system with management. They know how to move trains, and they know how to kick rears and take names, but in working with people effectively, they're pretty short. The program is humanitarian, and it's good public relations, contrary to the beliefs of most companies. It's good PR.

So it seems that "kick ass and take names originated in U.S. military slang, either in World War II or within 17 years after it, and that it became standard lingo during the Vietnam War and spread into civilian culture from there.

Taking names and numbers [or addresses]

A different wording that the OP may have had in mind is the phrase "taking names and numbers [or addresses]." This phrase goes back much farther than does "kicking ass and taking names"—but it has a fairly literal meaning, and I'm not at all sure that it qualifies as an idiom rather than as a common or set phrase. The two earliest matches that a Google Books search produces for this phrase are from 1879 and 1880. From Deposition of J. M. Freeman, jr. (February 14, 1879) in Papers in the Case of Mackey vs. O'Connor (May 7, 1880):

You swear positively that not more than two hundred voters cast their ballots at the Palmetto engine-house poll subsequent to your return from the supervisor's office?—A. That is my opinion.

Q. Do you know that from positive knowledge?—A. I know it from the manner in which they were voting.

Q. You did not take names and numbers subsequent to your return? — A. I did not.

And from debates of the Constitution Act Alteration Bill, in [Australian] Parliamentary Debates, Session 1880 (June 3, 1880):

Mr. WALKER. The new Council will represent two-thirds of the people of the country. ... When I offered myself for Richmond at the last election, I came before a great many of the people as a comparative stranger, and it was therefore necessary that I should send what I may call my election programme by post to every elector, taking names and addresses from the electoral roll.

Conclusions

The liveliest idiomatic expression involving "taking names" that I'm aware of is "kicking ass and taking names," an expression that may have originated in the 1940s and certainly existed by 1962. In military use the sense of the phrase is that soldiers subjected to such treatment are punished first by being manhandled in the traditional Sergeant Snorkel vs. Beetle Bailey manner and second by being written up for formal demerits in a report that goes up the chain of command.

A different "taking names" wording that is sometimes heard is "taking names and numbers [or addresses]." It is a fairly straightforward set phrase that means simply "obtaining contact information—that is, names and addresses—from people for some record-keeping purpose."

You most likely mean "kicking ass and taking names", which means having multiple victories over a number of opponents in quick succession, with a pace showing that this feat is not over yet. "kicking ass" means completely conquering an opponent, usually to a humiliating level, basically "kicking their ass". On the other hand, "taking names" refers to marking a number of individuals which have not been beaten yet, to be beaten later. It derives from the mafia, as taking names of future victims helps in finding moroe information andkeeping track of them. If that's not exactly what you were searching for, a deviation is "kicking ass in the morning and taking names in the evening".