Will the logo stay in mind?
For this test, you need the newly designed logo and the logos of competing businesses. All logos should be the same size, and may be glued on a cardboard so they're on the same background.
Ideally, there should be about 6 logos. For the execution of the recall test, pick a few viewers. Now present the logos to them consecutively, and have them view each logo for about 3 to 5 minutes.
If the time has passed, remove the logos again - otherwise, the viewers will remember the last image the best - and wait for about 5 minutes, then start the analysis.
Ask the contestants what they remember the best, which logos or parts of the presented logos especially caught their eyes.
Using these answers, you can generate a ranking of the logos, and see where your newly designed logo is in this ranking. You can also devise possible modifications to your logo, depending on the most striking elements.
This method is not particularly precise, but it can help you find out if you should apply some additional changes to your logo.