Yes. The lender can require the borrower to use a lender-selected provider. (This is not new under TRID. It was also the case for the GFE/HUD, though it rarely occurred.)
The lender can choose the provider; the lender can give the borrower a list of at least two providers and restrict the borrower’s choice to that list; or the lender can give the provider a list of at least one provider and allow the borrower to choose from the list or find a provider on their own (“shop”).
Even when the borrower chooses someone, the lender can still deny use of that provider when the provider is not on the lender’s internal approved list. (E.g. settlement agent has no access to Closing Insight or other collaboration portal as required by the lender; has failed to meet the lender’s “Best Practices” requirements, etc.)