Several Burkes as well.Could easily have changed the name to Berg or Burkhart or something.Not a major issue but you just know there is some continuity junkie out there trying to make the characters related somehow.

A little thought should be put into these things but maybe the producers aren't as interested in the small nlggly details as the fans are.
Sir
John Burke, the Royal Astronomer, was a distant cousin of San Francisco Mayor
Helen Burke (she married a British consul and businessman belonging to the ancient Burke line). Helen had no children that survived World War III, but Sir John did and had several generations that followed his interest in the stars and were some of the earliest colonists and boomers.
A direct descendant of Sir John, Yeoman
Harlan Burke, was one of the Khitomer conspirators, personally killing Chancellor Gorkon himself. He was killed by Valeris during the investigation, but left a huge black mark on the Burke lineage.
Harlan left children and grandchildren, shamed by his legacy. Three great-grandchildren of his, brothers Danny, Tommy, and Maxwell joined Starfleet in spite of this.
Danny Burke, the eldest, opted out of the Academy, instead enlisting as a soldier, fighting and dying valiantly during the Federation-Klingon War on Ajilon Prime.
Tommy Burke followed his older brother into the service, where his academic and professional skills went noticed. He earned commission as an Ensign and eventually a brief tour on the prestigious USS Enterprise-D as a relief tactical officer.
The youngest,
Maxwell Burke, joined Starfleet in the mid-to-late 2360s and quickly eclipsed both his brothers in rank and prestige, gaining an appointment as a lieutenant and first officer on one of the first Nova-class starships, the USS Equinox, in 2370. Unfortunately, the Equinox was abducted by the Caretaker the next year, and Burke would ultimately commit mutiny and murder in his attempt to reach Earth. He died in the Delta Quadrant, after tarnishing the Burke name once more.