Is it legal to have part of another company's name inside of your company name?

It's not a black and white issue.  Does the other company have intellectual property rights in the name?  Is your use of the name likely to cause consumers to be confused and think that you are affiliated with the first company (which depends on numerous factors - the types of businesses that are being operated, where they are being operated, the reknown and distinctivelness of first name, etc.)  For example, a restaurant can call itself "SloppyJoe's" even if there's a "Joe's" garage in the same neighborhood.  In your particular example, however, I think the use of the mark "hondalot" is likely to confuse consumers into thinking that "hondalot" is affiliated with "honda", and would therefore be prohbited.  "Hondalot" would be trading on the goodwill that honda has spent time and money developing, and would impair the value of that goodwill - any negative interaction which consumers have with "hondalot" is likely to diminish the value of the "Honda" mark, as will the fact that "hondalot" would be using the "Honda" mark without paying Honda for it.