Our top 5

Ezra is a favourite of mine but DP vetoed due to George Ezra who neither of us can stand- I didn’t even make that link!
Oscar is lovely but unfortunately very, very common.
Buddy is nice, for a dog...
Hugo is blahhhhh... just makes me think of a wretched Eton boy.
Ozzie -Osborne.

I think...
Oscar is a nice, pretty traditional name. He would probably come across a few his own age. Depends if you want a more common or unusual name.

Ezra has had an increase in popularity since pretty little liars so could date fairly quickly but I like the name.

Ozzie is neither hit nor miss for me.

Hugo I really like.

Buddy. I'm going to go the opposite way to other people. I know the fletcher family have called their child buddy and although I wouldn't choose it, I don't think it's an different to people calling their child teddy.

I would go for Oscar or Hugo

Oscar is nice, but it's very common and perhaps dated. The ones I know are in their 20s.
Hugo is nice, though I'm not personally very keen on it.
Ozlo is just very odd.
Why not use Oswald or Osbert and nn to Ozzie? I think Oswald could be good, actually.

Buddy is the name of a friends dog, so no!
What about Eli or Asher?

I’ve been a teacher for 30 years and never taught an Oscar although there is one in dd’s School.

Oscar: lovely, in our top 5 too.... not that unusual.
Ezra: love it!
Hugo: love it, not that unusual though.
Ozzie: shortened version of Oscar, doesn't really work as a stand alone name and I'm not keen at all.
Buddy: fab name, for a cocker spaniel. Awful for a human child.

In order-

Hugo
Oscar
Ezra
Ozzie & Buddy- these are not nice at all

FWIW I would much rather have a very nice if popular name than a twattish one.

Ozlo is illiterate and I can’t stand yoonique spellings. Buddy is dreadful.

Oscar and Hugo are very nice.

Oscars are often called Ozzie so I would just go with that.

I only like Hugo from your list. Buddy is awful.

I'm also a teacher and have taught many Oscars and Hugos.

I like Ezra. Haven't met one yet but can see it's one that could be working it's way up from pre schools.

Not too keen on Ozzie, Buddy or Ozlo but they do meet your criteria of not popping up in every school so, if you like them, I'd go with one of those.

How about Orson, Owen or Otis? Bryn, Blake or Bruno? Ellis, Enda or Ephraim? Solly/Solomon, Sage or Shay? Hector, Heath or Holden?

Oscar-lovely name, good alternative to Oliver. Quite a posh, classic sounding name.

Ezra- getting really trendy and popular, I'm not a fan.

Ozzie- great nickname for Oscar, Otis, Oliver etc but I can't see it as a name on it's own. I just think of Ozzie Osbourne.

Hugo- this was my top contender name, I love it. It's not unpopular, but it's not too popular. It's easy to say and spell and works on a baby, child or man.

Buddy- no. Sorry but it's way too cutesy. Unless you're a celeb or a raging hippy I just don't think it works.

Still love Oscar. Have you considered Otis?

From your list I like Buddy and Ezra best. Ezra is definitely on the increase though.
Osian or Ossian is a nice alternative to Ozzy

Ozlo would definitely be different!

Ezra and Oscar are quite popular at the mo. I know two baby Ezras.

Hugo is around but less common.

Tobias? Tobi for short 🤷🏻‍♀️

Felix

Buddy is quite cute but makes me think of Jamie Oliver

I really like Oscar and Ezra but as others have said they're far from unique and either very popular or likely to be very popular soon. I taught a little Oscar at my last school who was nn Ozzie and he was wonderful. I've never actually met an Ezra but I know it's tipped to be popular in a year or 2. I think of Ezra Pound and Ezra Keats when I hear it, who are both brilliant namesakes. Hugo is OK, but a bit wet IMO, a little bit "made in Chelsea". Ozzie is fine as a nn but I wouldn't use it as a full name myself. Personally I really dislike Buddy, I just think it sounds silly. Ezra and Oscar get my vote, but you'd have to be ok with not having a unique name.

Oscar (or Oswald) with nickname Ozzie could work?

I like Ezra and Hugo best.

Sorry OP, whilst Ozlo is definitely unusual I really don’t think it’s a good name. However you seem really keen on Ozzie and keep coming back to it so maybe you have found your name!

I love Hugo! It may (or may not) be worth noting that Ezra is the name of a character in the star wars rebels series that came out a couple of years ago, have no idea how popular the series is but thought I'd mention this as you said you didn't want something that could possibly become popular

Hugo or Ezra from your list. I’m not keen on Oslo or Ozlo - he could spend his life singing 🎶 ‘I’m Ozlo with a zee not Oslo with an ess’🎶

Ozzie is short for Oscar or Oswald. I like Hugo

Oscar, not Hugo.

I like Hugo or Oscar