I just checked the marriage certificates for 5 siblings of my grandfather, all who came to the US between 1910 and 1925. The names of their mother was the following -
Minnie Cohan
Miriam Colon
Mary Collins
Mary Collen
Mary Lock
Only the 2nd one was accurate. I think the variety was a function of the siblings 'Americanizing' their mother's given name and the clerk mis-hearing the name by the siblings who spoke with accents,
I have a great uncle here in the US who gave his mother's name as Ida Abrams on his marriage certificate. I found the original Russian/Hebrew marriage record for this woman, and her real name was Chaje Rabinowitch.
I have a great great grandmother who did come to this country, and she herself used the given names Minnie, Mollie, Mamie and Minnie in census records. Her Yiddish name was Michle. Her gravestone says Mollie. Her New York death certificate says Mamie. In a similar vein, a great grandmother of mine herself used the names Ruth, Sarah, Fannie and Louise Leapman in this country (!!!). Her children simply have 'Mother Leapman' on her gravestone. Find-a-grave lists her name as 'Unknown Leapman'. Her Yiddish name was Rochel Frieda, which is on her gravestone in Hebrew letters.
What I have found is that for women's given names in this country, there is a wide variety and it's not really clear to say which is correct or incorrect. I myself have had a difficult time explaining this to a second cousin who has a large family tree on Ancestry.
Michele Lock
Lock/Lak/Lok and Kalon in Zagare/Joniskis, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine in Trenton, New Jersey and Lida/Minsk gub., Belarus