AM1 it seems like these instructions could be very confusing for your respondent to understand and that you are making the respondent load harder on them. Can you achieve the results you want by either making this a ranking question instead of a rating question (if you need the respondent to pick one winner but don't want to lose who is next) or just ask for the name that fit very well:

https://www.qualtrics.com/community/discussion/comment/33804#Comment_33804Thanks, bstrahin, the client wants teh audience to assess around 7-8 product name options excluding 'other' and none. Do you think ranking could be a better choice?

AM1 at this point I would take your analysis into mind. What is your plan on how you report out about the assessment of the 7-8 product names? Do you need a winner? Do you need a degree of tolerance of each of the names?
The issue with your first matrix is that it is hard for respondents to understand what you want them to do and the scale is little so if you plan to look at means then all 7-8 names will have a value of 1-3, which isn't very wide. Even then it's a question if who is closest to 1 (fits well) because 2 (neutral) and 3 (not at all) aren't favorable responses. That's why I proposed narrowing the question to just select the options that fit well.
Depending on your analysis I think ranking could be good and give you more differentiation between the mean score for the names. But I would ask in two phases (1) which names fit with options for none and other then (2) rank the ones they chose - leave out other and if they say none consider if they should skip or be forced to rank their tolerance of the names.
If you are working for a firm, I encourage you to talk with your colleagues about how your firm would approach assessing this question on behalf of your client. You can learn more pros and cons that way and also have the weight of others behind your decision.