McCullum and captain Ben Stokes stayed in their roles after the Ashes despite calls for change because of problems on and off the field.
The first of three Tests starts at Lord's on Thursday and McCullum said: "We still want to be recognisable from the past, but we just want to be a cricket team which has evolved in some of the key areas where we've identified that we've fallen short previously.
"We want to be a team which is better under pressure, a team which can navigate tactically, that can understand where you sit in the game and what's required.
"We still want the identity of the past," he added, "but we want a more refined version of it."
England No. 3 batter Jacob Bethell, who made his first Test century in the fifth Ashes Test at Sydney, is fit to play despite having to cut short his time in the Indian Premier League because of a finger injury on his left hand.
"He was operating at gully in our training yesterday and he's absolutely fine, so there's no problems there," McCullum said. "He should be able to bowl as well."
Bethell has played six Tests, averaging 43, but only once on home soil when he batted at No. 6 and made six and five against India last year.
Now he is England's first drop, replacing Ollie Pope, but has a lack of experience in red-ball cricket. He has played only once in England's four-day County Championship since August 2024.
Off-spinner Shoaib Bashir will make his England comeback having not played at all on an Ashes tour he had been groomed for.
Ollie Robinson is expected to return to the Test XI for the first time since February 2024 with the remaining bowling place likely to go to Gus Atkinson ahead of the uncapped Sonny Baker.
ENGLAND (from): Ben Stokes (capt), Gus Atkinson, Sonny Baker, Shoaib Bashir, Jacob Bethell, Harry Brook, Ben Duckett, Emilio Gay, Ollie Robinson, Joe Root, Jamie Smith (wk), Josh Tongue.
