The SNP leader admitted the word "national" could be "hugely problematic".
Thousands To Re-Name Glasgow Hospital
It cost more than £100,000 to rename Scotland's newest superhospital.
Orginally called the South Glasgow University Hospital, the title was changed after a royal visit to the Queen Elizabeth University hospital.
An NHS spokesperson said: "It was considered a new hospital with a new name."
"In addition, the services from the new hospital would be used by the western catchment area north of the river as well as many people outside the south of Glasgow."
"It was therefore considered important to recognise the wider population being served and remove the geographical term ‘south Glasgow'."
NHS bosses say much of the cost came from the original budget and it was to take into account the wider area covered by the hospital.
The spokesperson continued: "The Non Executive members and senior nurses and doctors were supportive of the proposal and it was felt that this would be a suitable way to honour and appropriately mark the attendance of the Queen to open both hospitals"
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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