Just discovered your wonderful site in my frantic search for the perfect name for baby #3 (due September 6, but realistically, any day now!!). This pregnancy has flown by and we’ve been putting off the naming decision until now!So, our son’s name is Jack and our daughter’s name is Lila. Now we’re having another boy and have not fallen in love with any name. Well, I have fallen in love with one: James. BUT, it’s my husband’s name (although he goes by Jim) and he refuses to name our second son James for fear that later in life our firstborn son will grow resentful that he wasn’t given his Dad’s name. I think this is ridiculous thinking…but is he right? Can only the firstborn son carry the father’s name?So in lieu of James, I/we like Max, Charlie, Benjamin, Bradford, I also like Graham but I feel it clashes with our surname starts with ‘Gre’ and ends sounding like ‘fay’ (similar to the sound of ‘buffet’. I hope that makes sense)…it sounds very French when pronounced correctly (which is rarely!).If this were a girl, I love the names Georgie (Georgia) and Harper and Maggie…I hope you can help! Maybe it’s hormones and fatigue but I can’t seem to make a rational decision or even think straight at this point!
Although it's traditional for the firstborn child to be the namesake, there isn't anything inherently more worthy or important about the first child; I suspect the only reason is so the honor name is used at the first opportunity. If there's no reason for the children to believe that this third child would be particularly favored by his parents, I think it's likely the children won't much care---or if they do care, the caring could go either way: either "Why didn't _I_ get dad's name?" OR "Why didn't YOU have to get dad's name?" An honor name is a mixed gift: there aren't any specific benefits that go along with it (the benefits are more for the one who is honored)---and there are downsides, such as not having a name all of one's own, and dealing with any confusion that results from sharing.
One of my friends had twin boys, and they gave the father's name to the secondborn twin, so that each boy would have something: one boy is the firstborn, and the other is the namesake. It seemed like a good idea to me, and a good source of spin for other situations.
In this case, my bigger concern would be that the names Jack and James seem very similar, especially with a father Jim. Jack and Max also seem very similar to me, though a good fit style-wise.
Charlie is my own favorite from your list. Jack and Charlie are highly compatible names, but without being too alike. Benjamin is a very close second, especially if he'll go by Ben: Jack and Ben is a wonderful pair of brother names.
I also suggest Henry: Jack, Lila, and Henry.
Or Sam: Jack, Lila, and Sam.
I'm finding it a little challenging to find a brother name for a Jack. I think it's because Jack is a nickname name but also considered a stand-alone choice. So it feels compatible with other nickname names (Max, Sam, Ben, Charlie), but those names are not as often used as given names. So then having, say, a Jack and a Charles, or a Jack and a Benjamin, or a Jack and a Samuel, feels as if one boy has a good nickname and the other doesn't, or that only the nickname is the same style as Jack.
A name like Leo would be perfectly compatible with Jack---but I'm afraid it's too close to Lila. Drew might be perfect: it's short for Andrew but often used as given name. But I'm not sure it works well with the surname. Maybe Cole? It can be a nickname for Nicholas or Colton, but it's also given on its own. Or Liam---but again, probably too close to Lila.
Other nickname possibilities:
From this list, I think my favorite combination is Jack and Will. (Another post asked if "Jack and Will" would bring "Jack and Jill" to mind. I thought probably it would be a minor issue, and that it would be easy to say "Will and Jack" instead---but it's the sort of issue I like to mention so that you can think of it beforehand rather than afterward.) I like how all three children would have four-letter names, unless that would make you feel pressured for future children. Jack, Lila, and Will.