A political battle in Alaska has drawn attention due to its potential impact on the control of Congress. The issue centers on how many candidates with the name Dan Sullivan can appear on the state’s November ballot for Senate.

Dan J. Sullivan, a former teacher, is fighting to keep his name on the ballot against Senator Dan S. Sullivan, who is seeking re-election. The state’s elections office moved to disqualify Dan J. Sullivan, sparking controversy. Both Democrats and Republicans see his candidacy as more than just an unusual situation. Although Dan J. Sullivan, who says he registered as a Republican, is not considered a significant threat in the race, Republicans fear confusion among voters could assist Democrat Mary Peltola, a former Representative.

Lt. Gov. Nancy Dahlstrom of Alaska, a Republican, announced an investigation into whether Dan J. Sullivan coordinated with Ms. Peltola to confuse voters. Alaska’s top elections official, Carol Beecher, also a Republican and under the lieutenant governor’s oversight, challenged his eligibility to run. A letter sent from her office to Dan J. Sullivan required documents to prove his eligibility by a Thursday deadline.

Both Dan J. Sullivan and Ms. Peltola denied any cooperation to influence the election campaign. In response, Dan J. Sullivan asserted that the actions from Ms. Dahlstrom’s office appeared to be an effort to shield the incumbent Senator from facing a serious challenge in the election.