I have a large number of intake documents that all contain similar information. How can I create text boxes (or whatever) that are linked from page to page? I type the clients name on page 1 and all other linked boxes show that name?
You need to use fields for that.
You may fill e.g. document properties (File->Properties, fill some custom properties). Then you insert fields (Insert->Field->More Fields…->DocInformation->Custom) to the places you need. If you need them on fixed place on each page, then use frames with fields anchored to headers/footers, and positioned relative to page.
Another type of fields that may help is Set variable/Show variable/Input field (available on Variables tab of Fields dialog). See Variables - LibreOffice Help for more information.