What is the (English) word for two people born on the same day,
particularly for two people born on the same day of the same year?

The term "astro twins" (or "astrotwins") is sometimes used by those
who believe in astrology.

The term "same age" is what they tend to call people born on the same
day of the same year. ;)

tutuzdad-ga

how about if the two people have the same first name too?

I have heard the phrase "They have the same birthday" used to refer to
2 people who were born on the same day.

In academic studies, people with the same birth date are generally
referred to as belonging to the same "birth cohort", although the term
can be used (depending on context) to mean people born the same day,
month, or year.

Birthday twin or twins?
://www.google.co.uk/search?q=%22birthday+twins%22&hl=en&lr=&start=30&sa=N
://www.google.co.uk/search?hl=en&q=%22birthday+twin%22&btnG=Search&meta=

And whatever they are called, in a group of 24 people the odds are
better than 50% that there is a set of them present (not same year). 
Don't call me on that, but I read it somewhere once.