changed mac name after clean install 10.11 but...

hi guys,

yesterday I did a clean install of el capitan on my macbook pro and when i reboot i use a " new name " for the computer.

Now on iTunes Store there are all my devices but my mac have the old name. Now I want to know if this name will be updated automatically or not?

i checked on icloud.com and it is all ok.

Also in my iphone (settings-telephone-call to other devices) there are two macbook: one with the old name and one with new name but it is the same mac....

i hope that i explained, sorry for my english

thanks for the help