Do a bit of research on the company on the web. Are they owned by a much larger company? If so it is far more likely that they would try to protect their name, especially because its in the same field.
Now, if you go to something like legalzoom.com and register a new LLC or S corp with MovieMatchPro LLC or MovieMatchPro Inc, and you are allowed to do so by the state you are in, it is very unlikely that the company could do much as you are a legal entity, unless you try to copy what they are doing to a large degree and show no innovation at all. File a DBA in the city you are in to operate as MpvieMatchPro.com and go for it. Once you do that, your personal liability is very limited if they try to sue you, and you have the legal standing to run your business.
Also, think about other businesses. Open the yellow pages. You will see AA Acme Plumbing, AAA Plumbing, A Top Acme Plumbing etc. All are similar names, all perform same business and they all operate together. The difference is the large, established brand names who will protect their trademark and biz name, even if they know they are wrong and will lose. Its one of the things you have to do in biz to keep what you have - if you do not protect it, its gonna be taken from you by the courts.