First of all, I am gathering that you mean people born with both sets of sex organs

yes, that is what intersexed means. intersexed means those born with a mixture of both, there is no "standard" intersexed person. some are born with normal-looking penises and scrotums on the outside, but inside they have working ovaries and part of a uterus, and thus once they hit puberty they may start becoming "feminized" - meaning their ovaries are giving them estrogen, thus they are growing up with a male outside, but female "inside" - it may not make complete sense, but if it helps, most intersexed people have no idea what they should be feeling, or if what they are feeling is called MALE or FEMALE.

If so then I would also gather that they would know by a certain age which sex they likened themselves to.

then you would be wrong. many have no identification and simply identify as intersexed - they are neither male nor female, but both or neither.

That being the case, they could have surgery to become that what they believe themselves to be.

first of all, a bad suggestion - why cut your body up to make yourself what society says you SHOULD be? why put yourself at medical risk to simply force your body to conform to an arbitrary and literally fake ideal?  they were born that way and most do not want surgery - there are infants that the doctors "cut up" at birth so they "look" like a male or female, but guess what? most grow up to "feel" like the opposite sex that was chosen for them, or they don’t feel "right".

this is not a black or white issue - physical sexes can differ and they can blend, as evidenced by the presence of intersexed individuals.

Many people are born with extra fingers and such and they simply undergo surgery to remove the extra body part.

fingers are whooly different than genitals - as you know, people are JUDGED by their sex - males do this, females do that, only females can couple with males, only males can couple with females, ect… there are absolutely NO societal ideals concerning fingers or extra limbs. your analogy is moot.

People who are Homosexual, I fully believe, make that choice to be so.

and you are wrong. are you homosexual? if not, you should not make assumptions and judgements on a group of people you have absolutely no experience with.

but even IF homosexuals made the choice … what is the difference between them choosing which partner to be with, and intersexed individuals (who have both sex organs) choosing which sex to be regarded as? slippery slope…