I really like the name [name_u]August[/name_u] but would it be really odd or kind of lame since he would be born in [name_u]August[/name_u]? Or does that just not matter since most people in real life (as he grows up) won’t know when his birthday is?
I don’t think it matters — there are plenty of girls named [name_u]June[/name_u] who are born in [name_u]June[/name_u], and plenty born in other months. (For whatever reason, every [name_f]April[/name_f] I know was born in [name_f]April[/name_f].) You might get some people assuming that’s why you chose the name, but that’s more about whether it bothers you. It shouldn’t affect him in any way.
I think it’s fine to name him [name_u]August[/name_u] whether he’s born in [name_u]August[/name_u] or any other month! [name_m]Just[/name_m] like with [name_u]June[/name_u], [name_f]April[/name_f] or [name_f]May[/name_f]. 
Anyway, go for it! It’s not lame at all.
[name_m]Don[/name_m]'t think it is odd or lame but it is what you think that matters… and you really like it
I think it is completely fine! To close friends and family who actually know his birthday, the connection will be special & charming. And as you said, most people will not know or make the connection. It’s a great name & if you love it and decide it’s the one, don’t hesitate!
Sorry to burst the bubble, but it sounds a little lame to me… It’s my belief that people enjoy the unique things about themselves (age, birthday, hair color, name), and I think overlapping some of those things takes something away from that uniqueness. It’s really up to you, but that’s just my opinion! I can also see grade schoolers laughingly asking him if his birthday is in [name_u]August[/name_u] because that’s his name.
I actually think it’s really sweet idea. If you feel like it’s too much then maybe as a middle?
I have always wondered what the ‘rule’ was with names like this ([name_m]Leo[/name_m] also comes to mind, can only a [name_m]Leo[/name_m] be named [name_m]Leo[/name_m]? Should only a girl born in summer be named [name_f]Summer[/name_f]?)
Personally, I see no problem with naming a boy [name_u]August[/name_u] that is born in [name_u]August[/name_u].
You could ‘spruce it up’ by naming him [name_m]Augustus[/name_m] nn [name_u]August[/name_u], but if you will only ever call him [name_u]August[/name_u] then I don’t see the point. 
I always liked the idea of calling a baby girl [name_f]Autumn[/name_f] if they were born in [name_f]Autumn[/name_f] so calling a boy [name_u]August[/name_u] if they’re born in [name_u]August[/name_u] is lovely in my opinion.
You an definitely use the name [name_u]August[/name_u] if he was born in [name_u]August[/name_u].
We have an [name_u]August[/name_u] (although he goes by his middle name). We considered for our first but he was born in [name_u]August[/name_u] so we opted to save it. I felt like people would think we used it because he was born in [name_u]August[/name_u] and not because it’s such an awesome name!
That being said if you love it so much…use it! I don’t think it’s a dea breaker
I know I am like the odd one out here, but it does seem a little odd to me. Not lame, in that sense, but if my friend had a baby in [name_u]August[/name_u] and then called him that I know my first reaction would be “umm, why?? couldn’t you think of anything else?” - and I know that is not the case, and you obviously love the name. But it does put me off just a little. Sorry.
I don’t think it matters. After all, as he’s growing up, not many people are going to know what month he’s born in, are they? If you like the name, go for it…you can’t help what month he’s born in; don’t let that stop you!