May I please ask if you have the birth certs (or official transcriptions) for the children of Florence and Olaf OLSEN, and if so, what details were recorded on these re Florence? I would expect these to record the baby's:
Date and place of birth (if at home, the street address)
the baby's names (not their surname) and if present or not (so "present" indicating the baby was present when the birth was being registered)
Sex (Male or Female)
Father's name, occupation, age and birthplace (so first instance of a possible surname for the baby)
Date and place of marriage, and details of previous issue of the marriage (the full date, and the town, colony or state, nation etc. for the marriage and the full details for living issue recorded in chronological order by name (first name and then initials) and their then ages, then if any issue had already succumbed, their gender and number eg "2 males deceased")
Mother's name and maiden surname and age and birthplace (so if mother had been previously married, based on the info our OP has provided, this section should read "Florence Beatrice, formerly Anderson, nee St Clair" then her age and her place of birth ....
Then the informant's details (name, relationship to baby, and address) and the name of the midwife, and the details of the registrar/deputy registrar.
So if Florence was the informant, (and I would expect her to register the births, afterall her husband was apparently a mariner so likely often away at sea) then she ought to have provided FIRST HAND info as to her full name (including "Beatrice") and her maiden surname, and other details to help too. I have not yet found any evidence of the ending of Florence's marriage to Lawrence prior to the index details of the Olaf OLSEN marriage, so may I please again ask for the details from the death registration for Florence.
Cheers, JM