The user can determine their name.
According to an irreversible trend, use the universal their , avoiding the exclusive his and the clumsy his/her .
The Cambridge Guide to English Usage says: " their avoids gratuitous sexism and gives the statement broadest reference."
ell.stackexchange.com/users/None/
Just supplementing @Carlo_R.'s reply:
The following is from New Oxford American Dictionary
The word they (with its counterparts them, their, and themselves) as a singular pronoun to refer to a person of unspecified sex has been used since at least the 16th century.
In the late 20th century, as the traditional use of he to refer to a person of either sex came under scrutiny on the grounds of sexism, this use of they has become more common.
The use of they instead of "he or she" is common in spoken English and increasingly so in written English , although still deplored by some people.
ell.stackexchange.com/users/833/hjpotter92
He was once acceptable when you wanted to speak of a person whose sex was not known, or stated.
Now, it is considered old-fashioned, and other alternatives have been used.
He
/she Use he/
she
every time you are referring to a person for which the sex is not relevant.
singular
their Use a sentence like the following: "The user can determine their name.
"
Use the plural instead of the singular
In your case, it would mean to use a sentence like the following: "
The users can determine their names."
Somebody still consider the singular their not acceptable, and they rather prefer using the plural, as in the last example.
The Oxford Advanced Learner's Dictionary has the following notes about this topic: He used to be considered to cover both men and women: "Everyone needs to feel he is loved.
" This is not now acceptable.
Instead, after everybody , everyone , anybody , anyone , somebody , someone , etc.
one of the plural pronouns they , them , and their is often used:
Does everybody know what they want?
Somebody's left their coat here.
I hope nobody's forgotten to bring their passport with them.
Some people prefer to use he or she , his or her , or him or her in speech and writing: "Everyone knows what's best for him or herself."
He/she or (s)he can also be used in writing: "If in doubt, ask your doctor.
He/she can give you more information."
(You may find that some writers just use she .)
These uses can seem awkward when they are used a lot.
It is better to try to change the sentence, using a plural noun.
Instead of saying "A baby cries when he or she is tired" you can say "Babies cry when they are tired."
ell.stackexchange.com/users/95/kiamlaluno
I am guessing his name refers to a user name (on a computer system), right?
Anyway you can turn the statement around (passive construction):
The ( user ) name can be determined/specified by the user.
That avoids using possessive pronouns.
ell.stackexchange.com/users/None/
"His/her" is not grammatically correct.
It is a shorthand which used in a kind of abbreviated dialect of English that is found in instruction manuals and such.
A conjunction is required: his or her.
The user can determine his or her name.
Traditionally, male examples are used in English.
The example person is a "he" and that is that.
In English, the human race is traditionally called "mankind", a person fallen off a ship is "man overboard", tending to your job is "manning your post" and so on.
However, that kind of speaking and writing tends to make women feel excluded.
So this is why we use he or she for some unspecified person, or they .
But here is another strategy you can use in writing.
Simply use masculine pronouns in some examples, and feminine ones in others.
In some sections of the document, make the user female and use she and her (consistently: do not change the user from being a he in one sentence to a she in a related sentence): The user can determine her name.
Then in some other sections, make the user he .
This way you can avoid creating a sense that women are included, while avoiding repetitions of his or her , and without resorting to they and their .
Moreover, compared to using they , you create a more active sense that women are included.
Although using plural third person pronouns like they and their to refer to a single person is widespread and acceptable, it does not sound quite as good as using as singular pronoun for one person.
At least, subjectively speaking, not to everyone.
ell.stackexchange.com/users/197/Kaz
Should I use  his  or  his/her  in the following sentence?   The user can determine  his  name.
"His/her" or just "his"?
ell.stackexchange.com
<grammaticality><pronouns>
ell.stackexchange.com/questions/4831
ell.stackexchange.com/users/1254/user2208349
The word they (with its counterparts them, their, and themselves) as a  singular pronoun to refer to a person of unspecified sex has been used  since at least the 16th century. Use the plural instead of the singular and the users can determine their names.  The Cambridge Guide to English Usage  says: " their  avoids gratuitous sexism and gives the statement broadest reference." The use of they instead of  "he or she"  is common in  spoken English  and increasingly so in  written English. He/she' can be used but is deplored due to gratuitous sexism. Use 'they/their'.
You should use 'they/their'. He/she' can be used but is deplored due to gratuitous sexism.