Hii

Yes it is necessary that you write same spelling of you name, parents details, date of birth as that in your class 10th certificate.
This certificate is considered as the proof of your identity and the particulars mentioned in this certificate are considered to be correct and so while you fill up any form, you are supposed to give matriculation certificate with it as well.
If you by mistake enter incorrect detail in the form, correct that as soon as possible.
Incase your class 10th certificate has wrong details, contact the particular board from which you had appeared and make the necessary corrections.
Incase your application form has details which do not match with your class 10th certificate, there are chances that the application get rejected.

Hope this answers your query, feel free to revert back for any doubt.
Thanks!