• Fr. Thomas M. Reddington, 1964-June 28, 1983 [upon retirement]
• Fr. John V. Rosse, June 28, 1983-June 23, 1998
• Fr. Robert A. Klee, Jan. 1, 1989-Jan. 31, 1989 [Temporary administrator, sabbatical]
• David L. Bonin CPPS, Feb. 1, 1989-June 27, 1989 [Temporary administrator, sabbatical]
• Charles T. Manning, June 23, 1998-June 25, 1999 [Administrator] June 25, 1999-June 24, 2003 [Pastor; resigned]
• Michele Bertot, June 24, 2003-January 2006
• Sr. Joan Cawley, January 2006-June 2007 [Temporary administrator]
• Fr. John F. Gagnier, June 2007-June 25, 2013
• Fr. John Firpo, June 25, 2013-present [Temporary administrator]

On July 31, 1964, the parish called Church of the Holy Name (later "Holy Name of Jesus") was incorporated. Fr. Thomas Reddington was named by Bishop James Kearney to be the founding Pastor for this new parish serving the Southeastern portion of the town of Greece (as well as part of the City of Rochester). The first Mass was celebrated in the present church on October 29, 1967. The church would be blessed by Cardinal John Wright, then Prefect of the Congregation for the Clergy, a year later on October 28, 1968.

The parish became quite larger in the 1970s. Bulletins from the early 70s show attendance over 2,500, four priests on staff, and seven weekend Masses. As time progressed, and Catholics moved out of the area, each of these numbers would fall significantly. By the 2010s, Holy Name has been averaging around 300 weekend Mass-goers each week, and the number of Masses had been reduced down to two.

Discussion concerning the closure of Holy Name began as early as 2007, when the parish found itself $180,000 in debt. Parishioners worked hard under the leadership of Fr. John Gagnier to secure the financial viability of the parish, and soon Holy Name was debt-free and anually met the diocesan Catholic Ministries Appeal assessment. The financial security of the parish was not enough though, as attendance continued to decline and the future viability called into question. In the summer of 2009, the Eastern Greece/Charlotte steering committee recommended the closure of nearby Our Lady of Mercy, and called for a year-to-year evaluation of Holy Name. Fr. John Firpo was appointed temporary Parochial Administrator in June of 2013 and assigned the task of determing what should be done with Holy Name of Jesus going into the future.

In a decree dated June 23rd of 2014, Bp. Salvatore Matano announced the amalgamation of Holy Name of Jesus parish with St. Charles Borromeo, under the name of St. Charles Borromeo. A final regularly-scheduled Mass was offered September 21st, 2014. Holy Name will only be used for funerals, weddings, and other special ocassions until the church and related properties have been sold.