Verizon Galaxy S8 Group messaging

Hello, If I'm not listed as a recepient can I still see the group text?

No - unless a member in the group shows you or takes a screen shot of the chat and forwards that to non members of the group. Both alternatives are not courteous to the legitimate recipients who may expect privacy.

The way a group text works is like this.

The author of the original group text has a defined list of recipients. The author can choose how the recipients reply to their messages.
A) reply to all members of the group where everyone's reply contributes to the chat or
B) reply back to the original author where only the author can see the replies.

If you are not in the original group of recipients, then no. You can request to be added to the group mid stream but the author or (admin of a chat group like whatsapp) must add you.
 
I looked at the recepient list and did not see me listed, but I can see the group conversation
 
I looked at the recipient list and did not see me listed, but I can see the group conversation

3 things are possible.

A) On the author's device you may be seeing the message list in a non expanded view and when expanding the view you may be at the bottom, or

B) The original author might have your number in their contacts under the wrong name, or

C) You're looking at the list on your device and you won't see yourself.

Just block the sender if it concerns you.