Does court paperwork have to be in my 1st name? ie if my name is Jack, I use John instead of Jack.

No

Paperwork must be properly addressed with postage pre-paid to the intended recipient.^[1]

In criminal proceedings, the court may at any time correct an accidental slip or omission in a judgment or order, and a party may apply for a correction without notice.^[2][3]

If you get notice of the amendment, you have a right to oppose the application.^[4]

In civil proceedings, such as a traffic contravention debt, or a county court money claim, the court may allow an amendment to correct the name of a party, but only where the mistake was genuine and not one which would cause reasonable doubt as to the identity of the party in question.^[5]

^{[1] Section 7 of the Interpretation Act 1978
[2] Civil Procedure Rule 40.12
[3] Practice Direction 40B 4.1 to 4.5
[4] Practice Direction 40B 4.4
[5] Civil Procedure Rule 17.4(3)}