Can I link my old PS3 account to my new PS4 account?

Hi there.

So I created a new PS4 account, because I wanted a different name. I played through a couple of games and now that I still continue playing my PS3 once a while to finish some old games, I'd like to have that info display on my PS4 as well. Therefore I'd like to somehow link my PS3 account data to my PS4 account, is that possible?

I know in the beginning, while registering the new account it suggested that I'd use my old PS3 account to have all the data here, but I didn't so I wonder if it's still possible to add the data to my new account? If not, can I create a new account, using my PS3 account and then link the data from my current PS4 account to my PS3 account so that it has the trophies and stuff from the games I completed?

I don't think you can, you have 2 separate accounts now and I don't think they can be linked whatsoever.