We run an ecommerce site and the URL is our brand name + the product we sell, for example: brandnamesocks.com. Recently, the shorter url brandname.com became available so we purchased it and now it is our domain alias that 301 redirects to brandnamesocks.com. For a variety of reasons, we decided this was a better option than changing our site url. No problem there.
Now the owner of the company wants us to start using the alias in our advertising materials since it is shorter and simpler and presumably easier for people to see and remember. This would primarily be used in print advertisements, but will likely also appear in text links on our site and on the sites of bloggers/influencers that connect to our site. We understand that some services like Google ads do not allow destination mismatches, so in instances like that we would continue using the original domain.
Furthermore, the company owner would like to change our company email addresses to use the shorter domain even though it would not match the site's actual domain. This means that our support email, which has always been email@example.com would become firstname.lastname@example.org. Also, employee email addresses like email@example.com would become firstname.lastname@example.org. Yet the website would still be brandnamesocks.com.
All of our social media profiles use the name @brandnamesocks and the shorter @brandname is not available for any of them, so social media profiles would not change.
Our team is divided on whether or not this is a good idea. While we all agree the shorter name is simpler, some people are concerned it is not good practice to advertise a domain or email address that do not match the domain of the actual site. There is a concern about confusing customers and adding unnecessary complications that will haunt us further down the road, plus unpredictable SEO problems. Others do not think it will cause any problems as long as all of our redirects are in place. They do not think this will have any significant impact on SEO since the content of our site itself is not changing.
Does anybody have any insight on this? We can't find any solid examples of other websites dealing with this situation and we're wondering if these concerns are valid or if there are other issues we are not considering.