The phrase "adding him to the list" is correct and usable in written English.
You can use it when referring to the action of including someone in a group or a collection of names or items.
Example: "After reviewing the applications, I decided on adding him to the list of candidates for the interview."
Alternatives: "including him in the list" or "putting him on the list."
"Read these books and join me in adding him to the list, which each of us must compose on our own, of the world's very greatest writers".
The mayor of Springfield, Massachusetts, has called on the US State Department to stop the relocation of Somali refugees to his city, adding him to the list of mayors in the country who have rebuked the government's resettlement program in recent years.
A senior official said the United States would not hesitate to add him to the list if the violence did not stop.
Shaun Wright-Phillips is also surplus to requirements, although City would rather sell him than add him to the list of players who have been loaned out.
Harder's victory prevents Denham from returning for a fifth term and adds him to the list of California Republicans picked off in the midterm elections.
The surgeon said King had been evaluated for two years before a decision was taken to add him to the list of people suitable for transplant.
They explained that they were unable to put Mr. Aleynikov on the "no-fly" list, although they did add him to the list of individuals who have their international reservations monitored.
The board will then add him to the list of applicants, officials said, but it is not expected to take a formal vote on his or any other candidacy at this time.
Dzeko showed why City have been keen to add him to the list of players who have recently signed new contracts, with Pellegrini confirming that the announcement should be soon.
His resignation statement at 8.15 on Friday morning added him to the list of Tory prime ministers and leaders who had fallen in the Tories' never-ending European civil war.
His commanding officer chides him for his humorlessness, whereupon Tildy challenges him, too; and when the general in charge of the entire region intercedes on Tildy's behalf, trying to make him see sense, our hero clicks his heels and adds him to the list.
