Lee's office did not respond to requests for comment.
The resolution won't stop senators from placing a hold on a bill, but they will have to own up to the stalling tactic with their name appearing in the congressional record.
For years, senators have used holds to block nominees they dislike or as a bargaining chip in negotiations with fellow senators or the administration.
For the most part, those holds remained anonymous, but not always.
As an example, former Sen. Bob Bennett, R-Utah, disclosed that he temporarily placed holds on some of President Barack Obama's nominees for Interior Department positions after the administration pulled back 77 oil and gas leases in Utah.
On Thursday, the Senate also agreed to make it harder to order the reading of an amendment to block a vote on legislation. Lee and Sen. Orrin Hatch, R-Utah, were among the 15 Republicans who voted against that rule change, while 81 senators supported it.
These modest changes were meant to make the chamber more efficient and came after a group of freshman Senate Democrats failed in a bid to revamp the filibuster, a common tactic by the minority that requires the majority to get the support of 60 senators to move a bill to a final vote.