I just noticed that I have 2 different accounts on my computers. Is it possible to ask Apple to merge them and been able to share the music I bought on each account ?
There is no provision to re-sign the files that have been downloaded so by policy and by design, purchased items remain under the Apple ID used to purchase the item.
This means you can't divide up purchases after the fact (but you can agree to share the password and share the 5 authorized computers) even if you split up with a partner who shared an account with you.
You also can't "combine" past purchases - that account and password need to stay around and you can register a new "email" for communications of password resets but that original apple ID remains even long after you've left AOL or whatever name you originally used to purchase items.
Things have changed a bit since the accepted answer to this was written…
iCloud accounts cannot be merged, even now in 2019.
What you could do is set up Family Sharing & invite your old account to the "family", that way you can have legitimate access to purchases made on both accounts.