Hi. There are a lot of ways to accomplish this. For starters I'd suggest you check out "Allow creation of records in this table via this relationship." This is a checkbox in the FileMaker relationship graph that can let you create a related company, for instance, by simply typing the company name information into the field where the related company name would show up.
You can find an overview of this in FileMaker's built in help here:
Contents > Working with related tables and files > About the types of relationships > About single-criteria relationships
Note that this probably means showing the related company name *directly from the related company record* instead of as a lookup. By placing the company name field you looked up from directly on your registration layout, you can edit company names on the registration layout (a good or bad thing, depending on your prerferences) and create related companys by simply typing their name into this field. Selecting exiting companies would be done as you do now: whetever method you have for setting the company ID into your regsitration table sounds like its working.
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For a completely different approach, you can download the free version of CC Time and check out how we let you select an existing client or add a new one. New clients are simply added to the portal from which you select clients, then added to the time filter as if they already existed. Pretty simple approach; you can
see a screen shot of this here or
download CC Time to see how its done.
Hope that helps.