Firstly- apologies - the First marriage mentioned the name Collett

Both the Marriage licence & the parish record William signs it
CollettEvent Type: Intended marriage
Event Date: 28 Sep 1805
Groom: William Collett
Bride: Eleanor Hinton
Parish: St. Peter, Liverpool
Marriage: 29 Sep 1805
Groom: William Collett
Bride: Eleanor Hinton
However by the baptisms of their children, the name reverts back to Corlett
Baptism: 12 Aug 1807 St Nicholas, Liverpool, Lancashire, England
William Corlett - Son of William Corlett & Eleanor (formerly Hilton)), His Wife
Born: 26 Jul 1807
Abode: Toxteth Park
Occupation: Mariner
Register: Baptisms 1807, Page 326, Entry 1039
Source: LDS Film 93833
Baptism: 15 Apr 1810 St Peter, Liverpool, Lancashire, England
Mary Ellen Corlett - Daughter of William Corlett & Ellen (formerly Hinton))
Born: 6 Apr 1810
Abode: Lower Harrington St
Occupation: Mariner
Register: Baptisms 1799 - 1810, Page 266, Entry 1
Source: LDS Film 1656377
The trade directories of the time he was also listed as Corlett;
1807 (Liverpool Gore's Directory)
CORLETT, Captain William, 50 Upper Harrington Street, Toxteth
1816 (Liverpool)
CORLETT, Captain William, 8 Stanhope Street, Toxteth
1823 - 1841c
CORLETT, William, Pawnbroker, Stanhope Street, Toxteth