I'm not sure you support full names, but given Icelandic last names, all females end in -dóttir (or -dóttur for another form).
So checking for "dóttir" (and possibly without ó, e.g. "dottir"), which means daughter, is simple (male names end with -son, except for some foreign females who take their husbands last name; an exception in Iceland).
For some heuristics:
All given names in Icelandic ending in -a are female (except for "Sturla" that's a male name), such as Helga, Bára. [EDIT: Helgi, a male name, has Helga as alternative form, so it's not possible to know without context if Helga is female or not, the rule only applies for Normative declension what you would have e.g. in a letter addressed to you, see: https://ordstirr.wordpress.com/language/the-genitive-case/ and https://en.wiktionary.org/wiki/Wiktionary:Icelandic_noun_inflection-table_templates#Male_names ]
All names with Þ (thorn) or ð letter must be Icelandic.
I'm not sure you support full names, but given Icelandic last names, all females end in -dóttir (or -dóttur for another form).
So checking for "dóttir" (and possibly without ó, e.g. "dottir"), which means daughter, is simple (male names end with -son, except for some foreign females who take their husbands last name; an exception in Iceland).
For some heuristics:
All given names in Icelandic ending in -a are female (except for "Sturla" that's a male name), such as Helga, Bára. [EDIT: Helgi, a male name, has Helga as alternative form, so it's not possible to know without context if Helga is female or not, the rule only applies for Normative declension what you would have e.g. in a letter addressed to you, see: https://ordstirr.wordpress.com/language/the-genitive-case/ and https://en.wiktionary.org/wiki/Wiktionary:Icelandic_noun_inflection-table_templates#Male_names ]
All names with Þ (thorn) or ð letter must be Icelandic.