sender is always from the account used to authenticate with smtp server?

i've set up multiple accounts from two domains (gmail, and my personal domain). the default smtp server is set up to use one of my gmail identities. and when i send an email from any account, it displays as the sender the identity that i use to authenticate with the smtp server. for example, the identity set up to authenticate with the smtp server is abc@smtp.com. when i send an email from myname@mydomain.com, i expect the receipient to to see the sender as myname@mydomain.com. however, what is shown as the sender is abc@smtp.com. it doesn't matter what account i'm sending from. the sender is always abc@smtp.com. this can't be right.