Can we have the person filling out the form select info from Salesforce

Can we have the person filling out the form select info from Salesforce with a dropdown or something? We have a Company Name field that we want them to pull in the Account Name from Salesforce.

If I understand you correctly, you would like your users to pull data from their Salesforce account or yours?

Currently, the integration that we have is passing the submission data FROM JotForm to Salesforce. We do not have a way to pull data from Salesforce outside the integration. Here's a guide about our Salesforce integration: http://www.jotform.com/help/321-Mastering-SalesForce-with-JotForm 

If I misunderstood your concern, please do provide us more details on the process flow of your form or how it should actually work. We'll wait for your response.