Company pre-defined field is not showing up in field mapping

Company pre-defined field is not showing up in field mapping

When I convert a lead to a contact the company name is not able to be mapped to the contact. It isn't even in the field mapping list of fields. Should I delete the pre-made field and make a custom one as a work around or does anyone have a clue as to why it isn't mappable to contacts? 

Here is company in the lead field layout. 

However the field does not exist in field mapping. I am unsure how to go about fixing the issue without creating a custom field, so If you have an answer for using the default field please share it. 

As well as that issue I am also having trouble mapping lead description notes into contacts. For some reason they are not transfering either. 

The notes we all populated before I converted the lead into a contact. No idea where they went. This is my mapping
Surely Im overlooking something simple here I hope; Any advice is appreciated.