Gabriel Diya, 52, his daughter Comfort Diya, 9, and his son Praise-Emmanuel Diya, 16, are understood to have died in the triple tragedy on Christmas Eve.Mr Diya's Facebook account lists him as a manager of Open Heavens London, a Christian religious group with origins in Nigeria, based in Charlton, south-east London.
It is understood Mr Diya and his daughter are both British, while his son is American.
The three family members were found unresponsive in a pool at Club La Costa World on Christmas Eve, after the nine-year-old girl struggled in the water and her brother, 16, and father, 52, reportedly tried to rescue her.
Local reports said Spanish police were investigating the pump and suction system for a possible failure, but inquiries have found "no concerns relating to the pool in question", said operator CLC World Resorts and Hotels.
In a statement it said: "The Guardia Civil have carried out a full investigation which found no concerns relating to the pool in question or procedures in place, which leaves us to believe this was a tragic accident which has left everyone surrounding the incident in shock.