1st words of trademarks are more important than the 2nd words, etc., since that's how customers look companies up. And as the junior user, you probably wouldn't be able to get the name pass the USPTO's examining lawyers, and you might get a cease and desist letter from that competitor, even though they're not a "big brand."
You need to run the actual names by your own TM lawyer, who'd probably tell you that your feeling about what's confusing to customers isn't worth much, and whenever you want to use the same 1st word of an existing user's name to directly compete with them, you should choose another name,after hiring a TM lawyer to do a "knock out" search for viable and available TMs.
Don't make this important decision about branding your business without a TM lawyer's help, it's too important to your business and wastes too much time and energy and money if your instincts are wrong.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
There's also Starmark that's a large agency in our area among others. I would pick a stronger mark to begin with as given the number of folks using star for marketing already, you'll never be able to protect your mark as it will be too generic and your use too recent compared to others, plus you'll be subject to possible allegations of consumer confusion and trademark infringement from the other prior users.
When I see a question like this, I always wonder if the person asking it expects to get an answer that is free and that is legally sound.
It is quite possible that there are enough facts missing from the above description that it is not possible to give a correct answer. You know how they always say, "It depends."
How much is your business worth to you? What would it cost you if you had to get involved in a dispute? (Even if you "win.") Will taking this risk cost you less than getting a real answer from an attorney?