Change the sender's name in Mail.

I’m not sure of the details or of how widely the underlying problem might extend.

You can remove the mail account, and re-add it.

Your own info stored in Contacts is selected using Settings > Contacts > My Info

If the iPhone was never reset when transferred to you (if you didn’t start your usage from the “hello” setup), you will want to perform that reset now:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

You can back up your device contents, and then restore it after the reset.

Otherwise, you’ll be meeting a whole lot more issues including with apps and updates.

The reset will also transfer device ownership to you, as well.

If this reset was never performed, you will need the assistance of the seller to perform the reset, though the reset can be performed remotely.

Try removing and re-adding the mail account you’re using. You’ll need your mail server credentials.