Before each roll-call vote, members-elect are given the opportunity to nominate candidates by the Clerk of the House. They do so simply by stating that they are doing so; take for example the proceedings recorded in the Congressional Record before the first roll-call vote on January 3rd 2023:
The CLERK. Pursuant to law and precedent, the next order of business
is the election of the Speaker of the House of Representatives for the
118th Congress. Nominations are now in order. The Clerk recognizes the
gentlewoman from New York (Ms. STEFANIK).
Ms. STEFANIK Madam Clerk, on behalf of the House Republican Conference, I rise today to
nominate the gentleman from California, KEVIN MCCARTHY, as Speaker of
the House to lead America’s new Republican majority.
Stefanik then continues on in her speech, concluding with:
Madam Clerk, as the chair of the Re- publican Conference, it is my high honor to present our Conference’s nominee for election to the office of the Speaker of the people’s House, the Honorable KEVIN MCCARTHY from the State of California.
The Clerk then continues, allowing Mr. Anguilar of California to nominate Hakeem Jeffries, and Mr. Gosar of Arizona to nominate Andy Biggs before voting commences.
However, although these three candidates were the only ones formally nominated, members-elect are free to vote for any individual they like, without needing to nominate them to be a formal candidate beforehand. You can see this from the results of the first ballot. The individual doesn't even have to be a member of the House; according to the CRS report Speaker of the House Elections 1913-2021, votes were cast for candidates who were not representatives or members-elect in "1997, 2013, 2015 (both instances), 2019, and 2021".