Sorry if this isn't an appropriate place to ask.

well possible that it's a nickname, especially that of a child - in that case the given name may be repeated "for diminutive purposes" as is sometimes done in the case of women as well, but not quite as common for males (for any corrections or additions please add your comment).
"Real" given names with two repeated pronunciations or characters exist as well of course, the diminutive version is simply quite common.

The name could include 英, for instance, so for the nickname becomes 英英. It could also be a baby, a "婴婴".

Maybe it's also a nickname that is not based on a fixed name and character, writings could differ and shouldn't be that strict about the tone in that case.

This is one thing that I find quite annoying in normal life - seeing a pinyin name and not knowing the characters and/or tones for it.

Does anyone know a good site for looking up common names, which characters are used and which aren't?

I had a student called Ying1ying1, she used this character - 莺

As far as I know, there are not really standardised characters used for chinese names. You are going to have to just ask them what the characters are.

I did a quick Arch Chinese pinyin table check, most likely it is:

瑛瑛 or 莺莺 (female)
应应 (male)
英英 (male or female)

Some very common names not yet mentioned:
媖媖, 璎璎, 朠朠 for female and 霙霙 for male