Even worse if you use this domain as a way to track (and block) incoming e-mails. People at <FOO LTD> often have a hard time accepting that e-mail might actually be <foo>@<my name>.
I do this all the time, albeit with a qmail x-foo@ alias, and just straight up own it - "I sort my email so I can tell who sells my address". I've never really had a problem.
Ha yes, I get some inquisitive looks. I usually preface by saying, “This will sound strange, but I use a different email address with every company I interact with. So, it will be <foo>@…”