Writing your first and last name on something like an envelope is not inherently rude. In fact, it is quite common and expected in many situations, especially when sending formal or official correspondence. Providing your full name on an envelope can help ensure that the recipient knows exactly who the mail is intended for, especially if there are multiple people with the same first name within a household or organization.
Using your full name can also be seen as more professional and courteous in formal settings, such as business or legal communications. It helps establish a clear identity and avoids any potential confusion.
However, there might be some informal situations where using just your first name is acceptable, such as when sending personal letters to close friends or family members. In these cases, the level of formality and the relationship between sender and recipient will dictate the appropriateness of using the full name.
Ultimately, whether it's appropriate or necessary to include your first and last name on an envelope depends on the context and cultural norms of the specific situation. When in doubt, it's usually best to err on the side of formality and include your full name, especially when dealing with business or official communications.