Hi Ricky Raymond,

There are multiple ways to set the name field into the display name for Many2one.

You can set _rec_name for that model, you can use name_get method to print name field only etc.

In your case, For Partner, base code displays the name in Many2one using some specific context into the name_get ( for partner model its _get_name). 

Because your contact is a company, so that it use the _get_contact_name method and display the company, name as a Many2one partner name.

So for the Solution, you can override the "_get_contact_name" method and pass only name. It will solve your query.
Although for other, you can use the name_get method to set the name only.

Hope it will help you.