We are a group (unaffiliated to any organization or institution) of people willing to write a complaint/proposal to the local authorities, and we have formulated the text and everything. Since we are a lot of individuals, we would like to know how to sign this letter? Do we write our names and then sign? Or simply sign, without the name? Or delegate a "leader" who will take the responsibility? Can anyone help me with this? I can't find any example on this matter. Thank you!
Note: This answer assumes that you are living in a democracy where citizen participation in politics is allowed and encouraged. If you are living under an autocratic regime which persecutes political dissidents, you should disregard this advise.
When you are organizing a formal petition which is part of an official legislative process with a binding effect (like a popular initiative), then there will usually be guidelines about how the signatures must be made in order to be counted. Depending on jurisdiction, there might be exact requirements about what information must be added by every signer and sometimes there are even official forms to enter this information into. Consult your local laws for more information.
But judging from your comments, this appears to be more of an "attention petition" which is supposed to inform an official about a concern you have, but which has no legally binding consequences for them. That means there are no formal requirements per-se which you must fulfill.
The first thing any official will ask themselves when they read your letter is "Who are these people, and why should I care about them? Do they even exist or did the guy who wrote it made them up?"
That means it must be possible for the reader to confirm the identity of the people and that they are actually part of the constituency they are responsible for. That means anyone who signs the petition should not just put their signature, but also their full name and address.
By the way: You said you are unaffiliated to any organization. If you are serious about this cause, then you should consider forming one. It makes it much easier for politicians, media representatives and organization with similar interests to contact you.