Is signing my name to pictures that contain Hadiths, wisdom, or enjoinment of good, which I post on Facebook to spread good among people, considered showing off?

Writing one's name when spreading good is considered showing off (riya') if the intention behind it is to gain fame and status among people. However, if it is not done with the intention of showing off, then there is no sin in it. It is recommended not to write one's name when spreading good, as this is closer to sincerity (ikhlas) and more conducive to impact.