It is likely that Beechfield Street was called after Beechfield House. The following is an advertisement in the Belfast Commercial Chronicle on Wednesday 01 June 1831:
"A COUNTRY RESIDENCE
To be SOLD, or LET for a term of Years, BEECHFIELD HOUSE and LAND, situated innthe Vicinity of Ballymacarrett, residence of the late JAMES CALVERT. The Dwelling-House is New and Commodious, commands a full view of the Sea, and stands at an agreeable distance from the high-way. The Land, which contains Twenty-three Acres (House and Garden inclusive), is of choice condition, and the Office-Houses, which have been
recently rebuilt, are convenient. The House is ready for immediate reception of a Respectable Family. Application to be made to JAMES CALVERT, or to RICHARD BELL, Musgrave Street. Belfast, 5th Month, 30th,
"street off Mountpottinger Road, proposed to be called Beechfield Street, for W. B. Ritchie, J.P., and Mr. William Harper". (Town Improvement Committee, reported in the Belfast Telegraph - Monday 01 February 1875).
Beechfield Street was once called "Tom Thumbs Entry" according to James Patton in his book on Ballymacarrett.