Linking companies with contacts

Hi all as per my previous post i’m using Jetpack for my companies new CRM. I’m coming from a custom built access database so i’m importing csvs from exports from my old database. See below bullet points, could someone please advise?

I have 2 csv’s, one for my company database, and one for my contacts database, in the contacts database there is a field which has the company name for which the contact works at the company therefore creating a link in my access database.

I’ve purchased CSV imported pro and imported the company database, all has gone to plan and these are okay.

I have an issue with my contacts csv import, even if I map the field for the company name when importing my contacts, it does not link the contact to the company and as i’ve got 20,000 contacts, it would be impossible to go through and do them manually.

Can anyone help?

Many thanks!