If some fields aren't populating at all
Please have a user with Administrator permissions examine the permissions of the role you are in. If you have been assigned Read Only permissions to any fields on the accounts module then you will be unable to write into that field when converting. You will need the 'Write' permissions to be granted.
If a field has not populated as you expect
A field on a converted record such as an account will always default to the default set within studio, however it is possible at the time of conversion to amend this. We would recommend making this field auditable in studio so you can monitor user error.
Note: Related records, such as notes will not transfer over. This is working as designed and would need to be transferred to the new record manually