No, that is not possible. For starters, people may be connecting from no domain at all.
What you can get is the hostname (which can be set in the connection string, and not be relied on at all), the IP-address (which too can be spoofed, but this requires more work and skills) and the process id on the client (which presumably also can be spoofed),
It is very important for audit purposes when several people connect to SQL using the same SQL Login
If it is important to know who did it, stop using shared accounts and disable SQL authentication.
I should add that I have been in environments where I had first to log in to some web page with a personal account using an RSA token, plus a password that expired after 35 days or so. I think there was one more login step to connect for RDP to a machine. But once I was on that machine I connected to SQL Server with an SQL login that was shared by many. Since they had control how people reach the machine with SSMS, I guess they could connect the SQL login. But what if two persons were connected at the same time? What if someone inside the organisation "borrowed" that account?