"named" vs "that is named"

Solution 1:

There is a syntactic rule, called Whiz-Deletion, which is available in certain relative clauses.

Specifically, it can apply to clauses with the following properties:

1. the relative pronoun (which, who, that) must be the subject of the relative clause
2. the relative clause must contain a form of the auxiliary be immediately following the subject

Any relative clause that meets these criteria may, optionally (that means the speaker gets to decide, for any reason at all) delete both the relative pronoun and the auxiliary be form, as a unit. Because, as you say, they're redundant, which means predictable and carrying no information.

The funny name comes from the fact that the relative pronoun is usually a wh-word, and the auxiliary is usually is, so whiz deletion is just Wh-is deletion. The rule relates sentences like the first sentence in this answer with sentences like

• There is a syntactic rule, called Whiz-Deletion, available in certain relative clauses.

Solution 2:

Can I ask why you are phrasing it in such a way?

The completed action "named" is implied and not something that has to be spelled out once you share the name of the business--unless, of course, the action of naming it is something you need to highlight.

Entitled

Consider revising the sentence and order of ideas.

"In 2015 we established (add name here), a business that..."

"In 2015 we established (add name here)."