I can't find any info on whether this church had a name, besides the Wesleyan Church, but did find a bit on its history...
In January 1853 an acre of ground that was granted to James Macarthur by the crown, was given to Mr Thomas Denning for the purpose of building a Wesleyan Church. The church was built in 1868 and it was used on and off for many years by congregations of the Wesleyans, and later Methodists, for their services....and finally closed in the 1950's.
Several local people, interested in preserving the history of the village formed the Taralga Historical society in 1972. This group approached the Uniting Church NSW, with which the Methodist Church had amalgamated, and were able to obtain the old Methodist church as their headquarters. This church is now one of the buildings that is part of the Taralga Historical Museum managed by the Taralga Historical Society.