The principal characteristic group is expressed as a suffix. The name of the carboxylate anion alone (without the alcoholate function) would be ‘butanoate’. The name of the anion derived from the hydroxy compound (without the carboxylate function) would be ‘butan-1-olate’.
For the compound that is given in the question, one anion is chosen as the parent anion and the other one expressed as an anionic substitutent group. Since the carboxylate anion is the senior characteristic group, the parent structure is butanoate.
According to Subsection P-72.6.2 of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the prefix for the anionic group $\ce{-O^-}$ is ‘oxido’. (The prefixes is derived from the name oxide by changing the final letter ‘e’ to ‘o’.) Therefore, the name of the dianion that is shown in the question is 4-oxidobutanoate. The complete name of the salt is disodium 4-oxidobutanoate.