The 'from' address is the domain name, not outlook.com. You can set what the primary alias is within Outlook so you don't forget to change it before sending an email each time.
With regard to transmission of emails, here's what I see from my receiving email's source, I have zeroed out sender ip and removed my domain name, replacing it with "[domain.name]". I have bolded some points of interest.
Sent from my domain to my domain (in Outlook):
ARC-Authentication-Results: i=2; mx.microsoft.com 1; spf=none (sender ip is
000.000.000.000) smtp.rcpttodomain=[domain.name] smtp.mailfrom=[domain.name];
dmarc=none action=none header.from=[domain.name]; dkim=none (message not
signed); arc=pass (0 oda=0 ltdi=1)
Sent from my domain to Gmail:
ARC-Authentication-Results: i=2; mx.google.com;
arc=pass (i=1);
**spf=neutral** (google.com: 0000:0000:0000:0000::000 is neither permitted nor denied by best guess record for domain of [user]@[domain.name]) smtp.mailfrom=[user]@[domain.name]
If I change the MX record and promote my GoogleMail MX entries and resend from outlook to a personal Gmail account, then Gmail treats it as spam (received into spam folder, but with the hotmail MX record promoted to top of the MX priority that doesn't seem to happen when sending, it seems to be valid, albeit spf is "neutral" --I guess that's much better than "fail".