As rebmi stated you are very fortunate to have found records of other family, it’s just a coincidence that you are unable to find Dobson’s and that he didn’t serve in the France/Belgium theatre.
Re his name, the website you mentioned doesn’t seem correct, at least the page will not load; he’s listed as Condace on forces-war-records.co.uk and they are probably just repeating the CWGC’s information (more below).
He will not be recorded with his full name on the Helles Memorial, but simply as Gray D C; there’s 100 images of the Memorial at
http://www.ww1daleboys.com/apps/photos/album?albumid=2174025 , some are very clear but others are very hard to read.
In Soldiers Died in the Great War (SDGW) he’s listed as Dobson Coudace Gray and his place of birth & residence are given as Hendon and enlistment place as Sunderland.
In the GRO Index to War Deaths (Other Ranks) 1914-1921 the register reference is given as:
Name: Gray, Dobson C.; Rank: Pte; Number: 18566; Unit: Y.R.; Year: 1916; Vol: I.34; page 247
You can use that reference to obtain a copy of his certificate (not the same as Civil ones) from the GRO Southport via
http://www.gro.gov.uk/gro/content/certificates/default.asp or by post or phone (from above page RH side menu “Contact us”)
He’s listed as Gray, Dobson Condace in the Commonwealth War Grave Commission’s online database at
http://www.cwgc.orgIt should be noted that the CWGC’s online database was produced by using OCR software to “read” the official paper records and it is known there are a significant number of errors. With evidence, usually part of his record, but birth & marriage certificates may also be accepted, you should be able to get the CWGC record corrected. Contact them with a general query about his name being incorrect on their site but correct in SDGW, and see what they say.
You may already know that records on different web sites list him serving with the Yorkshire Regiment, Alexandra or the Green Howards. Always known locally and within the regiment by the nickname Green Howards, the regiment’s full title during the Great War was, Alexandra, Princess of Wales’s Own (Yorkshire Regiment). From 1921 it became The Green Howards (Alexandra, Princess of Wales’s Own Yorkshire Regiment).