Democrats have spent months engrossed by the slow-motion downfall of Senator Robert Menendez of New Jersey. But no sooner had he announced his resignation on Tuesday than their focus jumped to another question: Who would serve out his Senate term?

Party leaders had already been swapping names for weeks. Among them are a trio of prominent Black women; New Jersey’s first lady; and Representative Andy Kim, the Democratic nominee in November’s general election to replace Mr. Menendez on a more permanent basis.

The decision will fall to Gov. Philip D. Murphy, a Democrat in his second term, and advisers said he was winnowing his own list.

Here is what we know so far:

Menendez will vacate his seat in August

Mr. Menendez, 70, has been under intense pressure to resign since a Manhattan jury convicted him last week on all counts in a sweeping bribery scheme involving Egyptian intelligence, bars of gold and a Qatari sheikh.

On Tuesday, Mr. Menendez relented rather than face a possible vote to expel him from the Senate. He told Mr. Murphy in a letter that he would resign effective Aug. 20, giving the governor about a month to line up a replacement.

Whoever Mr. Murphy selects will serve until Mr. Menendez’s current term, his third, expires on Jan. 3.