Writing about how we decided to name our son without using any of the real names involved might be tricky, but I'm going to give it a try (Note: if you want to skip a lot of yammering about philosophies of naming and just see how we decided to name Kit, skip the next four paragraphs).
I've often noticed two main schools of adoption philosophy when I'm reading blogs and books, and I think the philosophy a parent leans towards can have a big effect on how they decide to handle naming. The first school is the philosophy of normalization, which is a reaction to the mainstream misconceptions that adoption is second best to having children biologically. This school wants to show the world that there's nothing weird about adoption and that adopted kids are just as important and just as loved as biological kids. The second school is the philosophy of reform, which sees that there's room for improvement in the ethics of adoption and strives to make progress in correcting where things have gone wrong. I think parents can belong to both schools, which is why I say "lean towards" one or the other and if you throw in other issues like race, it opens up whole new avenues of thought. I'm going to say right now that I think every parent has to make up their own mind on how they're going to handle it. I don't think our choice would be the best choice for everyone else.
The first choice is to completely change the child's first, middle and last names. Unless a child's older when they're adopted, I think most people change their son or daughter's last names to show that the child has become a member of the family. Changing the first and middle name can be an extension of that thought. It symbolizes that "this is now our child" no different from a child that enters the family biologically and follows the normalization philosophy. Of course, this isn't the only reason parents may decide to change their child's full name. In the case of some international adoptions, the birth name may not cross over well into the new culture. If a parent has grown up with an unusual, hard-to-pronounce name themselves, they may not want their child to go through the same ordeal. It's also possible that adoptive parents might have concerns about how other kids are going to react to the name when the child gets older and they'll change the name to prevent later teasing. It could also be that parents have just always loved certain names and just want to give them to their child.
Another option is to keep the child's name (usually changing the last name, though). In the philosophy of reform, this might be an act of respect towards the first parent(s), who go through so much suffering when they decide to place their child for adoption. Another way of thinking about it, is that the child's name is often the only thing they're bringing with them from their country/culture of origin, and parents might not change it so the child has some memento of what they've left behind. It's also possible that adoptive parents just fall in love with the child's given name or coincedently it was the name they were planning on using.
There's also a range of choices that fall in between the first two options. In the case of international/cultural adoptions, parents might decide to change the name, but use a name from the child's birth culture. They might change the first name, but make the surname of the child's first parent(s) the middle name. I think the most common decision and what we decided to do ourselves is to change the child's first name, but keep the original first name as the middle name.
Like Jack and Jill, Kit is a pseudonym and in Kit's case, it represents the first name we decided to give him. Kit's first name (not legally changed yet) is a name we've liked since before we even got married. It also happens to be a name used in English, German, French and Spanish-speaking countries, which covers most of the backgrounds of everyone in our budding family. There was more behind the decision to make Kit's given first name his middle name. While we were working on our adoption, Jill would visit photo lists of waiting children to ease her growing impatience. We had talked about giving our future child a Spanish name, but there were two she wasn't comfortable with. Both were very religious and one Jill felt became feminine in English (which is how a lot of people are going to read it here in the U.S.). When we got our referral, Kit's first name was the latter of the two I just alluded to. For a while, Jill wanted to keep Kit's original middle name as the middle name, but I convinced her to keep the first name, since it's likely that name meant the most to Kit's first mom (and honestly I like it better than his original middle name). We also talked about maybe fitting some other parts of his original full name in there, but since he's already going to have to deal with a hyphenated last name (we both hyphenated when we were married), we thought we'd better keep it short.
I should say that while we're keeping Kit's full legal name short, we'll always let him know that he has twice as many names as most other people. If he decides to change any of them legally when he gets older, or just decides to go by his original first name, we'll be fine with it. They're his names and he can decide what to do with them.