In a library context enquiry/inquiry management is different from most CRM systems which are designed to manage outbound sales and marketing interactions. Enquiry management for libraries is atypically about helping keep track of enquiries, facilitating follow up and maintaining statistics.

Some library systems may include an Enquiry management module. Eg the 247lib.com Library system https://www.247lib.com/247OPAC/DynamicPages/LibrarySoftware/247LIBINTRODUCTION

Bailey solutions provides an enquiry management solution ('Enquire') separatefor its library system offeringhttps:enquirymanagement.software/ Reftracker from altarama is a solution that is designed for libraries and information services http://www.altarama.com/Products/RefTracker.aspx

Reftracker for altarama is an enquiry management system designed for libraries and information services

http://www.altarama.com/Products/RefTracker.aspx

The are some general purpose system that might work in a library environment . eg from Evolutive
https://www.evolutive.co.uk/Enquiry-Management-software

Management of general enquiries in a library can be distinguished from online 'Reference Librarian 'services such as QuestionPoint.
NOTE: “OCLC has entered into an agreement to sell the QuestionPoint 24/7 Reference Cooperative and active
QuestionPoint subscriptions to Springshare, provider of the LibAnswers Platform. 31 May 2019 https://www.oclc.org/en/questionpoint.html