s/allows/allow/

maybe: ... which will allow to use the function associated with the name.
or: ... which allows to use the function ... (in this case, allows is fine)

That sentence is hard to understand.
Did you mean this:

The field which was set as the limit will be returned else it will be set to default values.

Is it just one group or groups (the variable says groups)?

I think you mean to write this:

The cap_grp_limit_groups function allows to limit access to groups.

How about this:

The names variable allows to limit groups by name and the gids variable by the group number.

The "respectively" has to move at the end, like this:
The names and ngids variables provide numbers of limited names and gids, respectively.

s/an/a/

s/Umable/Unable/

Same here...

... and here.

So we have a stracture:

struct group {
const char *gr_name;
const char *gr_passwd;
etc.
}

So if i limit it casper to gr_name, I still will get whole structure but only gr_name will be filled from it.

Just found this one: s/varlable/variable/

Ah, thanks for the explanation.
How about this then:
The field which was set as the limit will be returned, while the rest of the values not set this way will have default values.