There is nothing wrong with recycling these papers, so long as they are not exposed to any mishandling before the writing is erased from them. http://www.islam-qa.com/en/ref/4258/paper
How to deal with papers on which Allaahs name is mentioned
What is the sharias ruling about personal names found in newspapers etc that include either the prophet's name or Allah's name (Abdullah, AbdulKarim)? How may these papers be disposed of or destroyed?
These papers on which Allaahs name is mentioned should be kept and protected against being handled with disrespect until you have finished with them. When you have finished with them and no longer have any need of them, they should be buried in a clean place, or burnt, or kept in a place where they will be protected against disrespect, such as in a cupboard or on shelves, etc.
http://www.islam-qa.com/en/ref/21511/
These papers can be put to good use by giving them to people who can benefit from them, or placing them in a library for that purpose.
If that is not possible, or the papers are not suitable for that purpose, then they may be destroyed by burning or by cutting them up so that the verses of the Qur’aan and the name of Allaah disappear, or they may be buried. If a few words remain there is no harm in that.
There are machines that cut paper into long, thin strips (i.e., shredders), which may be used for this purpose.
http://www.islam-qa.com/en/ref/5390/
There is nothing wrong with you writing your name on papers and forms that you need to submit to others and there is no sin on you. Rather the sin is on the one who throws these papers into the trash, because that is showing disrespect towards the name of Allaah.
Shaykh Abd al-Azeez ibn Baaz (may Allaah have mercy on him) was asked: is it permissible to write the Basmalah (“Bismillaah ir-Rahmaan ir-Raheem – in the name of Allaah, the Most Gracious the Most Merciful”) on wedding invitations, knowing that they will be thrown away after that, on the street or in trash cans?
He replied:
It is prescribed to write the Basmalah on invitations and other kinds of letters, because it is narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Every matter of concern that is not started in the name of Allaah is bereft of barakah (blessing).”
And because he (peace and blessings of Allaah be upon him) used to start his letters by mentioning the name of Allaah.
It is not permissible for the one who receives an invitation which contains the name of Allaah or a verse of the Qur’aan to throw it in the trash or to put it in an inappropriate place.
It is not permissible to handle [Arabic-language] newspapers etc with disrespect or to throw them in the trash, or to use them as tablecloths or to wrap things in them, because they contain mention of Allaah.
The sin is on the one who does that, but there is no sin on the writer.
Majmoo’ Fataawa al-Shaykh Abd al-Azeez ibn Baaz, 5/427, 2nd edn.
http://www.islam-qa.com/en/ref/39376/paper
And Allaah knows best.
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