LoL yeah text messaging can be tricky commucating sometimes,I agree I dont have my dx with me today so I cant post a pic of what I am trying to say .
On my phone I dont use the gmail app for my other email account I have the other email app setup for that email account, it's shown on the default setup I think with the message folder and gmail folder.
When I acccess that mail folder from my phone not the gmail folder it shows my email being sent from that email address, and not my gmail address.(ex computer(default) email
myname@carolina.rr.com)
If I did accesss my gmail folder from my phone it would show it being sent from my gmail , email address. I dont know if that helped or if I confused you more trying to explain it lol but I tried

(ex gmail address
myname@gmail.com)
PS: I do have that email address synced with gmail and can toggle on the computer between the two(email addresses) as you mentioned in your post.