Nicola Sturgeon said she has been inundated with calls and emails to rename the airport after the Ayrshire-born Bard, but fears a change of name will confuse international travellers and dent ministers' hopes of returning the cash-strapped facility to profit.
The Scottish Government took the airport into public ownership last year after owners Infratil earmarked it for closure.
Ms Sturgeon announced a further £7 million investment for repairs and improvements at Holyrood's Infrastructure Committee today, but said it could be a long time before they see a return on the investment.
Ayrshire community groups and Burns societies have been lobbying for a change of name, and Ms Sturgeon said she has "had more emails and letters on this point than any other since we acquired the airport".
But she said the "hard-headed, pragmatic thing to do" is keep the current name for continuity.
"As somebody who hails from Ayrshire I recognise the strength of feeling over the issue of the airport's name and I very much welcome the engagement that the senior adviser had with the Robert Burns World Federation," she said.
"We have considered this issue very carefully, but on balance I have concluded that there are strong commercial reasons to retain the Glasgow Prestwick Airport name rather than looking to rename the airport.
"We need to keep in mind that changing the name would undoubtedly be a welcome move locally, but we need to promote and market Glasgow Prestwick Airport to airlines and passengers across the world.
"Glasgow and Prestwick are both strong names, as you would expect from an airport that has been operating for such a long time, and we don't want to risk creating confusion that would be more difficult to grow the business.
"However, the importance of recognising Robert Burns is not lost on anybody, and we will commission work to develop a Burns-related theme for the terminal and consider other ways in which the rich legacy of Burns can contribute to the promotion and the marketing of the airport."
She added: "The airport is not currently up for sale because we are in it for the long term and our intention is to secure a return on the public investment in the airport in the long term, and market the airport for sale on the basis of the turnaround that happens.
"So we have not set a date for that. There are too many variables at this stage and it wouldn't be sensible for me to sit here and give even a guesstimate date of when it will be possible to do.
"We're clear that it's a long-term investment, but a return to the private sector remains the end point objective.
"I was clear that we were not taking over Prestwick as some kind of ideological move or relishing taking Prestwick into public ownership. We were doing it because the only alternative was for the airport to close."