Annette,
Thanks for taking the time to copy the information.
If we take the first entry for 1845. He served as Mate (M) on a Sunderland registered vessel (port number 92) and the vessels port rotation number was 1060. The crew agreement was lodged with the port authority in June 1845. So it looks like he served on a coast trade ship. After that voyage, he served as Cook on a Rochester registered vessel with the port rotation number of 389. then as a seaman on a Sunderland registered vessel with the port rotation number 26. Finely back as Mate on the the Sunderland vessel PRN 1060
The key to finding out the vessels name is the port rotation number. Unfortunately, no key exists to link the PRN to a vessels name.
The only way to find this out is by trawling through the crew agreements for a particular year available by visiting TNA Kew. Series BT98, looking for him by name or PRN. Most of the vessels he served on were Sunderland registered so I would make a start there. There are 77 boxes in all, each containing approx 50 vessels. So there are are no quick fixes.
I attach the 1851 index's to give you an idea of the task.
http://discovery.nationalarchives.gov.uk/results/r?_ep=sunderland&_cr=bt%2098&_dss=range&_sd=1851&_ed=1851&_ro=any&_st=advTees,
There was no official registration of merchant seaman between 1857 and 1913. The Merchant Navy began to register its seamen again in 1913, in the central indexed register, or Fourth Register of Seamen. However, the entries for 1913 to 1917 have not survived. If he saw service from 1918 FindMyPast may have records. What you are looking for is ideally the name and official number of his last ship. It may then be possible to back track on his previous ships via Crew Agreements but you need to be very lucky.
A small collection of C/A's are at FindMyPast. I don't know about "Ancestry" Majority of C/A's for 1881 are on line here
https://www.mun.ca/mha/crew-agreement-links.phpand for 1915, here,
http://1915crewlists.rmg.co.uk/SW