A construction like "Substantiv ist zu Verb" can be used to describe a task, an obligation or similar that needs to be done to the substantive. For example
Die Blume ist regelmäßig zu wässern.
The flower is to be watered regularily.
Auf der Baustelle ist immer ein Schutzhelm zu tragen.
On the construction site, a hard hat is to be worn at all times.
Das Fenster ist geschlossen zu halten.
The window is to be kept closed.
Similar in Plural
Hunde sind an der Leine zu führen.
Dogs are to be lead on a leash.
This construction has a quite formal and authoritative vibe. You may find it in legal texts or similar, or on signage like the aforementioned construction site example.
In your sentence fragment, "des künftig zu bestimmenden Rechtsinhabers" is a further description of the "Rechtsinhaber", of the holder of rights. This holder of rights still needs to be "bestimmt", to be chosen, identified, determined or appointed. So you could say
Der Rechtsinhaber is künftig zu bestimmen.
The holder of rights is to be determined at a future time.
In your fragment, this means
(...) im Namen des zukünftig zu bestimmenden Rechtsinhabers (...)
(...) in the name of the holder of rights who is to be determined at a future time (...)