This isn't true but, there is some merit for the concern. The following quote, although argues a different issue, covers this (and I explain more about it later on)
Some businesses are worried that competitors will buy keyword oriented
domains thereby pushing their own site into obscurity. This can lead
to a panic shopping spree of domains. The idea is that as long as they
own the available domains, there is less chance of a competitor
beating them in the rankings. While there is some merit to this
tactic, it will have no effect on your SEO at all...
As you can read in the abstract article above, having the same or similar domain names doesn't mean it will have an impact on your site.
My advice, is you keep your business name and the domain name. Unless you both happen to be selling the exact same products, with the exact same descriptions etc, then Google will read the content and realise both the sites are unique and (assume) independent of each other.
Now, I can't view your site at work (it is blocked) but since the domain name has the words films in it, I'll assume you both have somehting to do with films. If you're both advertising films/selling films then this may be confusing for Google, especially if you're using the same films (the same content). However, even if that is the case, it still doesn't mean you'll be penalised, esepcially if your audience is different (EG, you only sell film to UK and they only to USA):
Websites that provide content for different regions and in different languages >sometimes create content that is the same or similar but available on different URLs. >This is generally not a problem as long as the content is for different users in >different countries. While we strongly recommend that you provide unique content for >each different group of users, we understand that this may not always be possible. >There is generally no need to "hide" the duplicates by disallowing crawling in a >robots.txt file or by using a "noindex" robots meta tag.
And lastly, since you're separate from the other company, I'm going to guess the content is different, despite the focus/topic may be similar. Even little things, such as spelling will help Google realise that the focus is for a specific demographic.