1) Both the father and mother have the right to name their child.
2) No other person (besides the parents) has the right to name the child.
3) Regarding which of the two (the father or the mother) has the first right to
name their firstborn child - there are differing customs. According to one
custom, the right to name the first child belongs to the father, the name of the
second child belongs to the mother, and so on, alternately.
4) Some say that this practice also fulfils the obligation of honoring one’s
father, if one names his first son after his father (i.e., the child’s
grandfather). On the other hand, if he fails to name the child after his father
it denigrates his honor; this entails a prohibition, and he will be punished for
it.
5) Some say that if one gives a name after some member of his father’s family
(not necessarily after his father himself), this also constitutes honoring his
father.
6) Others disagree, saying that only if the parents of the child do not have living
parents, they must first name a child after his father (i.e., the child’s
paternal grandfather), and not after his father-in-law (i.e., the child’s
maternal grandfather). However, if the child’s parents have living parents,
then the right to name the first child belongs to the mother’s family.
7) According to another custom, the right to name the first child belongs to the
mother.
8) Some have the custom that the name of a daughter belongs to the mother.
9) If a child is given two names, one after his paternal grandfather, and the other
after his maternal grandfather, the name of the paternal grandfather should come
first.
10) If the child’s mother gives him a name,
and later, the father arrives and wishes to give him a different name, some say
that the father can change the name. Others say that the name given by the
mother remains the authentic one, and the father cannot change it. Still others
say that the father can add a name, but not change the name completely.
However,
if they have suppressed the father’s name entirely, i.e., they have called the
child “ben …,” using the name of a man other than the father, then
the name given at the bris is null and void, as if the child had been
given no name at all.
11) If a girl is born, and her mother gives her a name (through her father - the
girl’s maternal grandfather - who went up to the Torah and gave her the name),
and the child’s father is in another place at the time (not knowing that they
would give her a name), and he gives her a different name, then the name given
by the father is the authentic one.
12) If the first son dies before he is given a name (i.e., before the bris),
then the right to give a name [to the next child] is retained by the one to whom
the right originally belonged.
13) If twins are born, and the one born first is weak, requiring his circumcision to
be delayed; and the second child is healthy, and is circumcised on time; then
the right to name this second son belongs to the one who has the original right
(even though this child was actually born second).