Typically in the US you'll want to check with your state about registring a D/B/A (meaning doing business as). Usually the fee to register is $50 or something minor and what happens is that you'll be mailed a certificate saying that name is linked to your LLC. From there you go to the bank and show them the document and they'll let you add it to your account.
Additionally you can even request having a separate bank account (something I've done to keep better records) but you also can just use the D/B/A to allow checks with the new name to go into your primary account.
Update: I'm in NY so the registration process might be different in MA (but not by too much) but essentially what you do is you go to the division of corporations and look up a "Doing Business As." From there you simply fill out a form to declare the name and link it to the main LLC.
Now this isn't going to be a separate company or entity but rather an alias. Similar to how you might have your email account at Person@xyz.com and then you have a forwarder of email@example.com linked to the main email - that's essentially the D/B/A - when people write an email to info - it still goes to you seemlessly.
Having a D/B/A will not affect your protections as it's not another business - just an alias and nothing more. As far as having a second bank account for the D/B/A - that's totally optional. I actually did that in my case because I'm incubating a professional organization under my company and wanted to keep separate books. Technically the separate account doesn't impact you except that you need to submit another tax document outlining the other account. In a legal sense however, that other account is still owned by your main LLC (that's why when I got my debit card for the D/B/A, it had my main LLC name on it)
After filing with the state, you'll get a certificate mailed to you (it can take a couple of weeks depending on if you pay for faster processing) of which you simply bring to the bank where you have your business account and they will link the D/B/A to your main account so that it can accept payments under the new name.