Stupid spellings bug me more.
Things like Sean/Shawn are fine, but Ashleigh? Name your son Alycks while you're at it.
I'm pretty sure Ashleigh is the most proper spelling of the name. Also, Sean is more proper than Shawn or Shaun.
June and August are good, strong Roman names. One should be proud to be connectdd to the Empire in such a way.
When my wife and I have a boy he will be named Julian after Emperor Julian the Apostate.
June and August aren't really "Roman names" though. August is a title, the name form of which is Augustine, and June is after Juno/Hera but nor really a personal name. Romans had
personal names like Paullus, Gaius, Marius, Titus, etc. So if you want to be really authentic I'd go with Paul, Mary*, Marc or something like that. Julian is a good name too, but it's a later Imperial period name**.
*The name "Mary" is actually the feminine form (Maria) of Marius which was a Roman praenomen. The biblical person's name was Mariam not Maria and mean totally different things. This was conflated to Maria when translated into Greek and Latin.
**The Julii were a particular family, and thus Julius was not a personal name but a "last name" as we colloquially call it today. So for example, people didn't call Julius Caesar "Julius" they would have called him Gaius. As a result to modernize his name it would be better to think of him as Gaius Julius like you would say John Smith. Caesar was actually a cognomen a sort of nickname. So for example "Eric the Red" the "the Red" bit is his cognomen. The word Caesar means either "to cut" or "head full of hair", but probably the later.