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Elwyn

I don't know about the twice bit. But Once was possible possible in all juristictions. Look at a birth cert image from England and Wales Column 10 is Name entered after registration in 1837 and on my mother's 1943 cert issued on the registration day. A baptismal name/ a forname can be added or altered up to 12 months after the birth by the 1953 Births & Deaths Act currently in force and the previous back to the 1836 Act (then up to 6 months after). https://www.legislation.gov.uk/ukpga/Eliz2/1-2/20/section/13/enacted
Also possible to re-register name/birth after Legitimization by subsequent marriage of parents.

forms and payment in appendix 1874 Act
https://www.legislation.gov.uk/ukpga/Vict/37-38/88/schedules/enacted

As Ireland used the Adaptment of Enactments to continue use of a lot of pre-partition legislation, was the same there, the 1863 Act + Births and Deaths Registration Act (Ireland), 1880, with a 12 month window. Parents not recognising the sacrament of baptism could also change a name themselves using Form B name not given in Baptism. 
https://www.legislation.gov.uk/ukpga/Vict/43-44/13/pdfs/ukpga_18800013_en.pdf [section 8 and Schedule 1 forms A,B,C]

From 1956 a TWO year window was allowed in Northern Ireland, that is different from England & Wales. https://www.legislation.gov.uk/nisro/1956/61/contents/made
But in Ireland under the Vital Statistics and Births, Deaths and Marriages Registration Act, 1952 there is no time limit.
"Registration of birth—removal of time limit for registration of name or of alteration of name." https://www.irishstatutebook.ie/eli/1952/act/8/enacted/en/html

Civil Registration Act 2004 (Ireland) still there https://www.irishstatutebook.ie/eli/2004/act/3/section/25/enacted/en/html#sec25

Scotland it was also possible to add a name after Baptism by the original 1854 Act (up to six months after, so the same as the original 1836 E&W Act).
An Act to provide for the better regulation of Births, Deaths, and Marriages in Scotland. [7 Aug 1854]
http://www.histpop.org/ohpr/servlet/View?path=Browse/Legislation%20(by%20date)&active=yes&mno=4048

XXXII. Name given in Baptism after Registration may be registered within Six Months. ...
and  XXXIII. Provision for Name given without Baptism after Registration. In the Case of any Child of Parents not recognizing the Sacrament of Baptism or Infant Baptism, it shall be lawful for such Parents or the Guardians of such Child, within Six Months after the Birth of any such Child shall have been registered, or if after Six Months, then only with the written Authority of the Sheriff, granted on a Statement of the Circumstances submitted to him, when any Name shall have been given to any such Child by the Parents or Guardians of such Child, other than that by which it may have been registered, to deliver to the Registrar in whose Custody the Register of the Birth of such Child shall be, a Certificate in the Form of the Schedule (E.) to this Act annexed, or to the like Effect, signed by such Parents or Guardians, whereupon, and upon Payment of a Fee of One Shilling, such Registrar shall, without Erasure as aforesaid, register therein the Name of such Child; and such Certificate shall be certified and transmitted by the Registrar to the Registrar General in the like Manner and to the like Effect as is herein-before prescribed regarding Certificates in relation to Names given in Baptism.

1836 England & Wales wording:
XXIV. And be it enacted, That if any Child born in England whose Birth shall have been registered as aforesaid shall, within Six Calendar Months next after it shall have been so registered, have any Name given to it in Baptism, the parent or Guardian of such Child, or other Person procuring such Name to be given, may within Seven Days next after such Baptism, procure and deliver to the registrar or Superintendent Registrar, in whose Custody the Register of Birth of the Child may then happen to be, a Certificate, according to the Form of Schedule (G.) to this Act annexed, signed by the Minister who shall have performed the Rite of Baptism, which Certificate such Minister is hereby required to deliver immediately after the Baptism, whenever the same shall then be demanded, on Payment of the Fee of One Shilling, which he shall be therefore entitled to receive; and the said Registrar or Superintendent Registrar, upon Receipt of such Certificate and on Payment of the Fee of One Shilling, which he shall therefore be entitled to receive, shall without any Erasure of the original Entry, forthwith register therein that the Child was baptized by such Name, and the Registrar shall thereupon certify upon the said Certificate the additional Entry so made, and shall forthwith send the said Certificate through the Post Office to the Registrar General.

The Registration of Births, Deaths and Marriages (Scotland) Act 1965 allows one change of name and one change of surname in respect of any one child after Baptism under clause 4, but sub-clause 5 for teenagers/adults wishing to eg adopt step-fathers name were allowed one change of name and three changes of surname https://www.legislation.gov.uk/ukpga/1965/49/section/43/enacted

Example of a baptismal forname change 1896 (bottom row)
https://irishgenealogy.ie/files/civil/birth_returns/births_1896/02176/1824139.pdf
Registered as Joseph Irvine Wetherall 13 Apr 1896 for birth 29 Mar 1896. David Irwin by baptism 3 Mar 1897.

Older registration forms had a separate column to add Christian names added after initial registration.

For that it was necessary to bring a baptismal certificate from the church signed by the minister and to pay a fee [as quarterly returns may have been already submitted and the entry had to be annotated with the change in both the Strabane ledger and any copy; GRONI then with head office in Belfast]. Many didn't bother. My Gran got through life and pension without a forname on her 1906 birth registration. Her 1919 paper copy to satisfy the Factory & Workshops Act regulations for 13-14 year olds has Margaret written the the Baptismal column by herself (different ink and hand from the rest).

Others got through life with a 'Certificate of Registry of Birth' or Short birth cert which has just the name + surname of the child, DOB, and District of Registration; no mother or father or place of birth. Thats what I used for employment and anything else as was the only copy I had after leaving home. My parents did have a full cert purchased on the day of registration too (1965), that I now have, but have not needed to produce so far. Which the passport office needed c.1980 couldn't tell you, thereafter it was renewed so not necessary.

those trees also have a death date for mother Margaret of 14 Oct 1962 in Bushmills and there is no registration nor for a James McKeown in 1962. Who started the chinese whisper is hard to tell.
https://ancestry.co.uk/family-tree/person/tree/110431456/person/102612424575/facts

1964 interred in Dunluce is a different James & Margaret https://findagrave.com/memorial/255610471/james-mckeown and they were of 55 Huey Crescent, Bushmills per death notices though that is what gets mentioned as a birth location for father James in the Meeke tree long before the street & houses appeared. Children don't match headstone (mind you the headstone date for James is 10th when he died 14th according to death notice and 15th according to GRONI). Don't believe it just because its carved in stone!

The date of birth on a death cert is only as accurate as the informant stated some disagree in one way or another from the actual birth cert, be it a year, month, or day out or all 3.
IrishGen and GRONI are from 2 different sources, the former the quarterly copies, the latter the original ledgers, whilst there could be transcription indexing errors on either, the chances of both doing so are slim and there is no birth for an Elizabeth McKeown on 19 June 1919 in N.I.

If you need a paper certificate you can get it from either GRONI or the Irish GRO for a birth in 1919. The old quarterly indexes (Findmypast, Ancestry, Familysearch) are no use to GRONI, they do not have any pre-partition quarterly BMD copies.
They are largely obsolete for ordering from GROI, Roscommon too. https://www.irishgenealogy.ie/view/?record_id=5fc6443d7a-445335 or see FAQ on IrishGen
You don't need mother's maiden surname at all for a cert, if tick the box on the search index. If you use the "Order a birth certificate" that has extra questions as most are ordering a recent cert for someone living.
https://www.rootschat.com/forum/index.php?topic=849427.msg7168488#msg7168488

No relationship to deceased is legally needed either on GRONI or GRO England to get a paper cert, can just enter none in the box and are presented with a payment page £15 for the paper cert.

Edit: have suggested an index amendment to mother Canning to GRONI.