You can use
REPLACE
to remove all spaces from a string (untested):
WHERE LCASE(REPLACE([Supplier_Pastel_Bank_Details.BD_Name], ' ', '') LIKE LCASE(REPLACE('%" & SupplierName & "%'), ' ', '')"
But I suggest to check the results manually to avoid false positives.
In your case it might be also necessary to ignore trailing dots like with "Company Inc." and Company Inc".