The boy is believed to be Kaden Reddick from Reading. He sustained head injuries at the Oracle Shopping Centre store on Monday.
Police said the boy's death was being treated as unexplained but not suspicious.
A spokesman for Topshop said the firm's thoughts were with the family.
"We are thoroughly investigating all the events surrounding this extremely sad situation," he said.
Officers remain at the scene and the shop was closed on Tuesday.
It is believed the accident involved a display in the store.
People turned to social media to pay tribute to the 10-year-old and his family.
One Facebook user said: "Love you guys,  the worlds going to miss you wee man and the amazing things you would have achieved in it."
Another said: "No words can describe or change what your going through just know we are all here for you , sending you all our love. You are all in our thoughts."
A third wrote: "That gorgeous smile. Kaden you are a big miss. Your mummy and dad need you to watch over them because they are hurt."
Police would only say that the boy was from Reading and that officers were supporting his family.
Det Supt Paul Hayles said: "We continue to investigate the circumstances surrounding this death, a scene watch is in place at the Topshop store and is likely to be in place for some time.
"Detectives are now working with the local authority and the store owners to gather all of the information on how this incident happened."
A bunch of flowers was left by a passer-by against the shop's closed shutters.
A card, which was unsigned, read: "RIP little man. To the family. Please take home if you wish x."
South Central Ambulance Service sent three ambulances and a rapid response vehicle to the scene, on what was the first day of the half-term school holiday in Berkshire.
The boy, who was found in a life-threatening condition, was taken to the Royal Berkshire Hospital but later died.
Reading Borough Council confirmed it was investigating alongside police.
The Health and Safety Executive said it was not yet involved.
A date for a post-mortem examination has not yet been set.
Clothing retailer Topshop said its board and staff were "deeply saddened" by the "horrific" accident which killed a boy aged 10 at one of its stores.