Nothing to worry about on that aspect. It's all in the guide.
Here's what's stated:-
Here's the form1.5 Enter your surname or family name as you want it to appear on your certificate.
1.6 Enter your other names as you want them to appear on your certificate.
1.7 If the names shown in section 1.5 and 1.6 are different from the names shown in your passport or they are spelt differently then please explain why on page 13 of the
application form.
At the end of the form it states:-
Means marriage certificate.If the name you are currently using is different from the name on your passport or travel document you should send evidence of the change of name
Here's the form Guide
Do be sure to read through all the questions on the form and all the corresponding guidance notes. Especially those concerning Supporting Documents as there is some key information.
Take a special note that the ID used for Life in the UK test must also be enclosed with the naturalisation application.
Hope that helps and Good luck