Welcome back to Just Answer.
David Alonzo's parents were William L. WILCOX b 24 May 1808 Portage Co., OH d 28 Jul 1892 Lemonweir Twp, Juneau Co WI and Phylura RANDALL b 23 Jul 1806 Watertown Twp., Jefferson Co., NY d 26 Jan 1893 Lemonweir Twp, Juneau Co WI who were married 16 Jul 1830 in Jefferson Co., NY.
William L's parents were David WILCOX b 1772 Jefferson Co., NY d 25 Mar 1860 Lewis Co., NY and his first wife Lorena HOPKINS b 1774 VT d 4 Aug 1838 Jefferson Co., NY.
David's (b 1772) were Nathan WILCOX b 1747 in RI died before 1823 and Rebecca MOON b 1752 in Washington Co., RI, who were married 1772 in Washington Co., RI.
Nathan's parents were William WILCOX b 1731 RI d 02 Jul 1805 Windham Co., VT and XXXXX XXXXX b 1737 VT d 20 Nov 1788 RI.
William's (b 1731) parents were Stephen WILCOX b 1692 Washington Co., RI d 26 Jun 1766 who were married 1714 in Washington Co., RI. XXXXX XXXXX's parents were XXXXX XXXXX (1694-1755) Rhode Island and his wife Susannah (maiden name unknown).
Stephen's parents are in dispute. They could have been 1.) Thomas WILCOX (1664-1728) and Mary HAZARD (abt 1665-dead) or 2.) Stephen WILCOX (1670-dead) and Elizabeth CRANDALL (1675-aft 1704) or 3.) Edward WILCOX 1662-1750) and Martha HAZARD (1666/1668-1753)
All three boys were the sons of Stephen WILCOX (1633-1690) of Washington Co., RI and his wife Hannah HAZARD(1636/7-1685) who were married 1658 in Newport Co., RI.
Stephen WILCOX b 1633 was the son of the immigrant Edward WILCOX b 1600 in Sussex, England d 13 May 1638 Washington Co., RI and his wife whose name is XXXXX XXXXX were married 1632 in Newport Co., RI.
Edward was the son of John WILCOX d 1651 England and his wife (name unknown.
So, the name appears to be English rather than Polish.