The Swedish musician, 79, who is a founding member of the pop group, comprised of Ulvaeus, Agnetha Faltskog, Benny Andersson and Anni-Frid Lyngstad, said they share it with a "very famous herring factory in Sweden".
Speaking to Gyles Brandreth on the Rosebud podcast, he said: "As we were kind of famous, all famous in Sweden, we made our first records under Agnetha, Benny, Bjorn and Anni-Frid.
ABBA achieved worldwide fame after they won the Eurovision Song Contest in 1974 with Waterloo. (AP PHOTO)
"And the DJs on radio and everywhere else, in our office, they got tired of saying that ... as you can imagine.
"So they just abbreviated it to the initials ABBA.
"We didn't have a choice in the matter. I thought it was such a stupid name. And it is.
"It's also the name of a very famous herring factory in Sweden - marinated herring, big thing in Sweden.
"And we had to ask them for permission to use the name because they had the name.
"And then they said 'As long as you don't dabble in marinating.'
"I thought we should have a cool name like The Rolling Stones or something like that, The Northern Lights.
"And here we are with ABBA."
ABBA are the most successful Swedish act of all time in the United Kingdom charts, having scored nine number one singles.
The group achieved worldwide fame after they won the Eurovision Song Contest in 1974 with their hit song Waterloo.
Last month they were made Commander of the First Class of the prestigious Order of the Vasa in Sweden - the first time it had been given in almost 50 years.
Earlier in May, Eurovision returned to the country but the band did not reform and instead, their digital ABBA-tars from the ABBA Voyage show played as an interval act during the competition through a recording from London.
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