I adopted Izuho about a week ago, but I decided I want to make a different Lumos with a name that I picked out, but I still want Izuho to get a chance for a nice home, so I've been training his stats. When my account is old enough to take him to Delphi again, will his stats stay trained if I leave him there and will he have a better chance of getting adopted?

Yes, his stats will stay the same when you abandon him but I'm not sure it will necessarily give him a better chance of being adopted. It wouldn't hurt but I have to say it's probably not something I would bother with, personally c: Though I also don't feel like sticking any more money into my own battle pets either at this point so xD

Thank you for the help! And your username is really cool :)

You're welcome, and thank you! ^_^

after a pet gets stats of 2000 dropping them into the Adopt R Us will result in a lost of 10% of its stats, but before then no effect on stats from abandonment. Adopted pets (and transferred too?) cannot be battled with for a month after adoption. So nobody will be really looking for stats when they adopt.

If you're putting sP into training maybe put sP into buying CSC for a name-change?

That would be great! Except I already made another pet with the name I wanted, but I guess I could get one for a future name. What does CSC stand for and how much does it cost?

C ash S hop C redits. These are how the site supports itself. You can either use your own USD (or use a service that will do an automatic currency exchange for you if you are not unitedstatian) in RL, or you can find someone here who already has done this and is selling Credit Gift Cards in their user-shop or Trades.