No reliable records have been found to indicate her surname or her ancestry.

The following baptism occurs BEFORE Phebe's birth, so must be for a different person of that name:

New York Births and Christenings, 1640-1962
Name: Phebe Wood
Event Type: Christening
Event Date: 13 Mar 1725
Event Place: Huntington, Suffolk, New York, United States
Event Place (Original): First Church, Huntington, Suffolk, New York, United States

It is often claimed without proof that Phebe Lamoreaux is the daughter of Brnjamin Wood and Catherine Covert.

U.S., Dutch Reformed Church Records in Selected States, 1639-1989
Name: Benjamin Wood
Event Type: Marriage
Marriage Date: 16 Jul 1715
Marriage Place: Collegiate Church, Manhattan, New York, USA
Spouse: Catharine Covert

Benjamin Wood may be the son of Jeremiah Wood and Susannah Pine. He was born in 1688, probably in Long Island, New York. He appears in the August 31, 1698 census for Hempsted, Long Island, New York with his parents and siblings. According to "The Covert Family", Fischer,et al., 1989, he later removed to Northcastle, Westchester County, New York. O'Callaghan, in "Lists of Inhabitants of Colonial New York". p 258, lists Benjamin in Capt. Jacob Hick's Militia in 1715.

Catherine Covert is NOT the same person as the wife of Thomas Bird (son of Andrew Bird of Somerset County, New Jersey) who is shown in the 1719 will of Jan Teunnise Covert as Catherine Bird (See Below). Some genealogies state that Catherine Covert married first Benjamin Wood, however, the birthdates of the children for both Thomas Bird (ranging from 1707 to 1731) and Benjamin Wood (ranging from 1716 to 1725) overlap, so there must have been another Catherine Covert who was the wife of Benjamin Wood and who married at the Reformed Dutch Collegiate Church in Manhattan on July 16, 1715.

https://archive.org/details/covertancestry00jone
Covert ancestry
by Jones, Edson Salisbury
1906
Page 6
'Will of "Jan Kuvers" of Millstrone, Somerset Co., N. J., yoeman, stricken in years, dated May 2, 1719, and pr. April 13, 1723, names wife Jane, sons Tunis (eldest), Bergon and Lucas (youngest); and daus., Catherine Bird, Orianchy Couser (bap. "Ariaentje"), Jane, Marry and Bathseba. Signed "Jan koevers." (East Jersey Wills, A., p. 124, and original will.)'

Pierre Lamoreaux and Phebe Wood were married in October 30, 1748 in New York ["The Mercereau Family" by George E. Sawyer, 2001 pg 4]. They had 10 children, all born in Phillipstown, Putnam County, New York.

Jane (27 Jul 1749 - 1820) m. Gideon 'James' Florence, Jr
Isaac (29 May 1751 - ) m?. Phebe Rumsey, m. 2 Mar 1790, Hannah Prindle (dau. of Benjamin Prindle and Hannah Marshall)
Joseph (11 Oct 1753 - 11 Nov 1840) m. 27 Nov 1782, Abigail Sneden
Luke (5 Mar 1756 - aft 1820) m. Phebe Crossen
Peter (13 Oct 1758 - ) m. 4 Jul 1782, Martha Crow
Susannah (16 Aug 1761 - ) m. Robert Davenport
Phebe (10 Jun 1763 - ) m. 13 May 1783, Moses Clark of Harvastraw
Jesse (15 Jul 1765 - bef 25 Mar 1816/7) m. Charity _____
John (31 Jan 1767 - ) m. Abigail Mapes
Andrew Walker (29 Jan 1771 - bef 25 Mar 1816/7) m. Hester Horton