Assume nothing. Personally, I wouldn't consider Menachem and Nechama to be the same name.
I know of several cases where siblings had the same name - usually they are named after a deceased grandparents and first one died very young, so the parents tried again to honour their late parent.
I have cases in my family where two sisters had the names Lina and Lena. Both survived to adulthood and married. This was in Germany in the 1820s and 30s.
My 5-greats grandmother was sometimes called Rachel, and sometimes Reigelene. She had a sister, about 3 years younger (unless I have the births mixed up), sometimes called Reigelene, and sometimes called Rachel. Both survived to adulthood and married. This was in Metz, France in the 1740s, and yes, I do have copies of their birth records (one says Reikle and the other Rachel).
But we only have the written records to go by - we don't know what they were called at home.