Garraway or Wright, Dunfermline or IOW ?

I’m needing some help here, but the story is not a short one.
Richard Garraway was a soldier in the New Zealand Army during the First World War. I know what happened to him, but would like to learn his heritage. I have been chewing away at this for about 8 yrs.

I have his war records, but more questions are posed than answered. Date of birth recorded is 3 October 1887, and my enquiries point to him being born on Isle of Wight or Dunfermline, Scotland, but I can find no such birth record. I do have information that does link the two locations.

The 1891 census records a 2 year old Dick Wright living with Mary Broy Garraway (46) and her husband Ambrose Garraway (48) at Newport, Carisbrook, Isle of Wight.

Dick's relationship to Ambrose is recorded as "Nurse Child." The fourth member of the household is Ambrose and Mary's 25 year old son, James. A second son is John, who appears in census records at another address in Newport.

Ambrose died in 1892, and Mary Broy Garraway, widow of Ambrose Garraway died at Lilliehill House, Dunfermline on 13 February 1900.

Did Mary take the young Dick Wright to Dunfermline and did he become Richard Garraway ?

I can’t find either on the 1901 or 1911 census. (By 1912 Richard was a coal miner on the west coast of the South Island, New Zealand)

The birth cert for Dick Wright records he was born on the 4th of October 1888 at 53 Castle Road, Newport, Isle of Wight, in the county of Southampton, England. This is one day one year away from the day of birth on Richard Garraway's army record.

Dick's birth was registered on 22 October 1888 by his mother, Annie Wright, formerly Wilson. His father is listed as Frederick Wright, a Building Contractor.

Can anyone help with any information on these two ?

I do not require any further information on any of the Garraways unless a link can be shown to Wright or Wilson.

Cheers, Fred.