changeing the name that the iphone shows when a text is sent

"A text"?

You cannot change the name when sending an SMS or MMS text message. (Perhaps you could through your cellular carrier, but very likely not).

You can change the name when sending an iMessage. That is done at Settings > Messages > Send & Receive > Start New Conversations From

The name that shows on someone else's phone when you send them a text is entirely dependent on what they have your name listed as in contacts. For example, if I have your phone number in my contacts and have listed your name as "potato", that's what will show when you text.