If your name is similar to a larger companies name and you even do a similar thing to what they do. Where is the line that is crossed legally stop?

This sounds like more of a trademark than a copyright question, as it seems that you are concerned about your company name and/or logo (brand) infringing another company's intellectual property rights.   Where trademark infringement is concerned, the issue is whether your mark is or would be "confusingly similar" to the mark of the existing company.  Since a trademark identifies the source of goods or services, might people who saw your trademark be confused and think the goods or services you offer are coming from the other company?  If you do offer goods or services that are similar to those offered by the other company, and your mark is likely to cause confusion about the source of those goods or services, you could have a problem.   You say that the name you plan to use is one word, while the other company's name is two words.  That could be adequately distinguishing under some circumstances, but it would require comparing the two to try to make any sort of prediction.  There are ways to lessen the similarities between trademarks; it would be necessary to see what you're working with.  It's a relatively subjective issue as to when the line is crossed such that there is a likelihood of confusion, but that is the line. Another potential issue could be trademark dilution, if your mark were to lessen the uniqueness of a famous mark, but the existing mark must be shown to be in fact famous.  I don't know enough about your company to know whether its mark would meet the rather high bar of being considered "famous."