Police can confirm that the 58-year-old man found dead at Lakefield Place, Llanelli, was Gary Williams from Gowerton.
The 46-year-old woman also found dead inside the property was Jessena Sheridan from Llanelli.
Officers were called to Lakefield Place at just after 8.30pm on Sunday, December 29.
The police investigation will not result in any criminal prosecution. The matter has been referred to HM Coroner, who will open inquests into both deaths on January 3.
The families wish to be given privacy to grieve at this time.
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