But the anti-lobbying rhetoric and policies did not discourage some former Trump aides from seeking big paydays from the influence industry, where few of the established players had close connections to Mr. Trump or his inner circle.

Some Trump insiders, including Mr. Cohen and Corey Lewandowski, a former Trump campaign manager, positioned themselves as strategic advisers. Because they were offering insight — or political intelligence — on Mr. Trump and his team, and not overtly lobbying, they did not need to disclose their role with Congress and possibly the Justice Department.

AT&T fanned out to try to keep pace in this changing climate. Although the company has long retained a platoon of lobbyists with deep connections on both sides of the aisle, none of the firms they worked with were as close to Mr. Trump as Mr. Cohen.

The company said Mr. Cohen had approached it about being a consultant, and that he was among “several consultants” the company hired as Mr. Trump was assuming the presidency.

AT&T officials would not disclose the names of the other people and firms hired. But according to a person with ties to Mr. Trump’s campaign, AT&T approached other Trump associates about possibly retaining them as government affairs consultants or lobbyists. The person would speak only under the condition of anonymity because the talks were private.

Among Trump associates pitching AT&T was Mr. Lewandowski. AT&T said it was approached early in January 2017 by Avenue Strategies, a lobbying firm that Mr. Lewandowski helped found. AT&T said it did not pursue a contract with the firm, which Mr. Lewandowski left in the middle of 2017.

AT&T paid a total of $4.1 million in lobbying fees to nearly 30 firms through the first three months of this year, according to congressional lobbying filings. But none of those businesses, including top-tier law firms like Mayer Brown and Akin Gump Strauss Hauer & Feld, have lobbyists who were as close to Mr. Trump as Mr. Cohen.