There's no means to text with a Gmail address that'll show a Gmail address in the SMS, unless the sender adds that address into the text of the message.
If this is Apple Messages, then that Gmail address is likely an Apple Account.
If you don't want the messages, or they're causing you concerns, block the sender.
Block, filter, and report messages on iPhone - Apple Support
Many folks will filter unrecognized senders. That is described in that link.
If there's a legal issue potentially arising here whether civil or criminal, best contact a victims' rights group, legal representation, or — if they're an option for you — local police, depending on the details.
if this is headed for a legal case, screenshots or a screen recording video of scrolling through the Messages conversation is commonly used to archive chats.