Converting a lead and linking to existing company throws an error

I have a brand new lead and I save it.

I qualify it.

I go to conversion and auto-create New Company, New Contact & New Opportunity.

All GOOD so far.

Now in our data hierarchy, an existing customer can expand and add new Ship To locations/sites to an existing parent company.

In that case,

we create a new lead and during conversion

They should link it to the original Parent Company and auto create a new opportunity.

This is where we are facing issues

- Should the text field "Company Name" on the Leads page have the same exact name as the parent company we are linking to during conversion or can it be different?