You can click on the table name in the dbml table and rename it. Or you can select a table in DBML and go to the properties window. There you can change the name and table to which it connects.
One way to avoid name clashes is to designate namespaces accordingly. For example, you can put your DBML file in a subfolder in your project and assign it something like DataAccess. Therefore, when comparing with the Ling2Sql class, you should use DataAccess.Customer, and you can avoid a conflict with the Client, because he lives somewhere else.
As a tidbit, Linq2Sql by default makes tables not multiple. This is based on convention. For example, in the customer table there are many customers. When you create an instance of an object, you look at one Client, not a table. The object is essentially displayed in a row in the Customers table, so it becomes the only one.
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