If a prisoner's full name was known he would be tried under that with the alias recorded as well or vice versa if it was an alias of long standing. For sentencing purposes the judge would always need to know about any past offences the prisoner might have. As Harry/Henry Green was openly Harry Green on the 1891 census and visited in prison by his wife, it doesn't seem possible that the authorities wouldn't know his real name.
Marriages Dec 1890
Green Henry Wandsworth 1d 1016
Jutsum Fanny Wandsworth 1d 1016
Harry Green was aged 19 on the 1891 census (no Harry/Henry Green of the same age born Battersea on the 1901 census). Census night 1891 was 5th April.
but there appears to be no record of the hanging
http://www.capitalpunishmentuk.org/contents.htmlfull list - of hangings at Wandsworth 1891-1901
21st July 1891 Franz Munch aged 31 for the murder of Jane Hickey
19th August 1891 Robert Bradshaw aged 56 wife murder
11th October 1892 John James Banbury aged 22 for the murder of Ann Emma Oakley
18th June 1895 Joseph Canning aged 32 for the murder of Jane Youell
2nd July 1895 Henry Tickner aged 42 wife murder
4th February 1896 William Morgan 56 wife murder
5th January 1897 Henry Brown aged 32 wife murder
3rd May 1899 Frederick Andrews aged 45 wife muder
4th October 1899 Robert Ward aged 27 murder of two daughters
19th March 1901 George Parker (Hill) aged 23 for the murder of William Pearson
13th August 1901 Ernest Wickham 30 for the murder of Amy Eugenie Russell (girlfriend)
There were two Richard Greens with births registered in Wandsworth registration district in 1891
Births Sep 1891
Green Richard Wandsworth 1d 755
Births Dec 1891
Green Richard George Wandsworth 1d 600
No Green deaths in Wandsworth registration district in 1891 for any Green male near Harry's age, or any Harry or Henry.
Wandsworth prison registers are held at the London Metropolitan Archives.
The Times did cover executions at Wandsworth, though not necessarily all the trials.
James Berry hanged 6 men at Wandsworth prison between 1885 and 1891
http://www.capitalpunishmentuk.org/wands.htmlBesides the two already listed in 1891
http://www.capitalpunishmentuk.org/contents.htmllists 4 other hangings at Wandsworth, 2 in 1890, 1 in 1889 and 1 in 1885.
I have a copy of 'My experiences as an executioner' by James Berry first published in 1892. He doesn't mention Henry Green, but then he doesn't list all the people he hanged in his 'career' (131). He retired in 1892.
'In March 1892 Berry wrote his letter of resignation, probably without knowing that in October of the previous year the Home Office had already decided that "the employment of Berry as Executioner should no longer be recommended to the High Sheriffs".'http://en.wikipedia.org/wiki/James_Berry_(hangman)
'His final execution was carried out at Edinburgh on the 11th of January 1892 when he hanged Frederick Storey. James Berry was not popular with the Home Office because of his drinking, holding 'court' in a local pubs after executions, and his behaviour at the hanging of John Conway within Liverpool’s Kirkdale prison on the 20th of August 1891. Berry resigned in early 1892.'
http://www.capitalpunishmentuk.org/hangmen.htmlWho did Fanny go onto 'marry'? Have you found her on the 1901 census?
Regards
Valda