I understand that trademark/service mark is to claim rights to use a mark/service. However you don't always see it beside the logo, I just wonder when do you need to put it on, and when you don't?
I am not a lawyer. If you are seeking legal advice regarding trademarks, consult a trademark attorney.
The ™ symbol is used to notify others that you intend to register the mark, phrase, icon, whatever.
The ™ offers no legal protections whatsoever. It merely serves as notice to anyone who see the item that you will, at some point in the future, register the item as unique to you or your company. This provides others the opportunity to either alter their own items or contact you about any possible likeliness or duplication.
After a period of time displaying the ™ you can apply for registration. The period which the ™ needs to be used varies and it is best to consult a trademark attorney for specifics based on your needs.
There is never any specific legal requirement to displaying the ™ (or SM) it's basically just groundwork for further action later and there's nothing which states that further action must be taken. Levis still uses a ™ on many, many items even though they've been around for decades.
To address @Dom's comment -- no, you don't have to pay to use ™. Anyone can use it at anytime. You do have to pay the Library of Congress to file copyright documents (that's for document filing. Your work is copyrighted the moment you create it). And you have to generally file and pay for registration ®. But use of the ™ is free since it is merely a notice not a legal protector.
None of this is meant to be legal advice. If you are seeking legal specifics as they relate to your work, you should always consult an attorney.
™ is symbol for Unregistered Trademark https://en.wikipedia.org/wiki/Unregistered_trademark
It depends what you want to impart on your branding. Trademarks have various purposes depending on your IPO (intellectual property office) of your state/region/country.
Visit your IPO then you can decide wherether or not you want to put trademark symbol or what type of symbol you'll place.