I have been told that the name Ekberg means in Swedish 'Oak Mountain'.
In my own family's case, my grandfather told the story that an ancestor of ours was in the Swedish Army, and was in a unit that had a lot of 'Nilssons'. The commander of the unit was tired of yelling, 'Nilsson, do [this or that],' and getting most of the unit's attention.
So the commander told my ancestor his name was now 'Ekberg'. This was probably Hans Nilsson Ekberg (1840-1895) who married Kjersti Nilsson Ek(1843-1932).
My grandfather was from Malmo, Sweden. He emigrated to the US, and so there are Ekbergs in California, USA. I have also found Ekbergs in Minnesota, Florida, and Texas, USA.
I have been told that the surname Ekberg is not uncommon in Sweden. I have also heard the there are quite a few in Finland.