For example, if one is using multiple pens to write something and has not used one of them in awhile, one may think it is "feeling" "left out" and so will switch to use that one. A logical mind KNOWS that inanimate objects cannot feel but one may have such empathy for all things - living or not - that one may attribute human feelings and emotions to them and an emotional brain does this automatically. It is not a conscious action, it is automatic and it dictates how one interacts with things. One can use a logical mind to recognize it but stills feel compelled to make sure everything is taken care of and included. Is this a specific disorder or just a piece of one of another disorder?
Interesting question. I have thought about this a lot, and while I cannot offer a conclusive answer, I can offer some ideas that stem from scientific literature.
I should note that this question may technically be considered off-topic, as it seems to be looking for a diagnosis (and self-help questions are prohibited on this website). However, for the sake of my own curiosity and the curiosity of others, I'll provide my answer nonetheless.
To answer your specific question: No, there is no officially-recognized disorder that causes one to assume human emotions in objects. To be fair, the condition you have described does not constitute the definition of '[mental] disorder' because, by definition, a mental disorder is a mental or behavioral pattern that causes suffering or poor ability to function in life. On the contrary, it seems that this behavioral pattern of yours is helpful to you, for reasons that I will explain below.
There is a theory that the brain forms an image of the body's homeostatic sensations in the "primary interoceptive cortex" of the brain. This area is located in the insula, which is linked to emotion (the body's homeostasis), as well as empathy.  This theory is supported by fMRI imaging, which shows activity in the insular cortex when one is asked to feel one's own heartbeat, or empathize with the pain or emotional state of others.  Coincidentally, the insula is also involved in psychopathology, or the study of mental disorders. Specifically, it is linked to anxiety disorders  and emotional dysregulation. 
The spindle neurons found at a higher density in the right frontal insular cortex are also found in the anterior cingulate cortex, and it has been speculated that these neurons are involved in cognitive-emotional processes that are specific to primates, such as empathy and self-aware emotional feelings. While the mechanisms behind the insular cortex are not well known, it is thought that these functions arise as a consequence of the insula's ability to relay its internal 'homeostasis' (or its overall well-being) to the conscious observer. 
Given the evidence that empathy is associated with insular activity, and given the evidence that the insula regulates the body's internal sense of 'homeostasis', it can be inferred that those who are highly sensitive (i.e. highly attuned to their internal level of homeostasis) are automatically highly attuned to the others in their environment, as well. Thus, there may be a tendency to expect similar levels of sensitivity in other things, and (by proxy) there may be a tendency to 'tread lightly' around others due to an automatic assumption that they are similarly sensitive. This may extend to inanimate objects, if one recognizes that the 'environment' that the object is in is not maintained in the body's subjective view of homeostasis.
Another thing to consider is that young children often show attachment or subjective association of feelings to objects, and that this is considered normal in young age because of the positive effects it seems to have on children. One study found that children who attended day-care full-time were significantly more likely to develop attachments to inanimate objects than children who only attended day-care part-time. It is not certain why this is the case, though it can be speculated that increased exposure to the real world (and time away from the parent or guardian) increases the child's anxiety as they learn to become independent. A prior study found that there was no link between behavioral disturbances and object attachment; on the contrary, another study found that children used object attachment as a mechanism for arousal reduction (and, thus, anxiety-reduction) in the face of adversity or discomfort in the environment.  As I mentioned before, it is thought that children use these objects to transition from dependence to independence.
This is different from treating objects as if they were people, because this is essentially using the object as a token of security to replace the mother as the child advances in age, thus allowing the child to become independent. However, it may reveal insight into those who naturally associate objects with emotions, because it may represent an underlying anxiety in the individual. The attachment to the object may be a way for the individual to circumvent that -- though it could also be unrelated, as this is still in a speculative stage.
Overall, however, I would say that this behavior does not implicate disorder in an individual. To the contrary, it appears to be a soothing mechanism. If I had to make an informed guess based on the information above, I would theorize that those who continue to associate emotions with inanimate objects outside of childhood may simply have stronger natural insular activity, and thus a stronger tendency towards one's internal 'homeostasis', or emotional activity. Because the individual is naturally more sensitive to the environment / emotional affect of others due to heightened activity in the insular cortex, they naturally attempt to regulate the environment's 'homeostasis' based on the individual's own bodily concept of homeostasis. Thus, if you were to feel left out if you were a pen that was not being used, then you may very well treat every pen the way you wanted to be treated. :)
 Emeran A. Mayer (August 2011). "Gut feelings: the emerging biology of gut–brain communication". Nature Reviews Neuroscience 12: 453–466.
 Benedetto De Martino, Dharshan Kumaran, Ben Seymour, and Raymond J. Dolan (August 2006). "Frames, Biases, and Rational Decision-Making in the Human Brain". Science 313 (6): 684–687.
 Paulus MP, Stein MB (August 2006). "An insular view of anxiety". Biol. Psychiatry 60 (4): 383–7.
 Thayer JF, Lane RD (December 2000). "A model of neurovisceral integration in emotion regulation and dysregulation". J Affect Disord 61 (3): 201–16
 Passman R. H. (1976). Arousal reducing properties of attachment objects: testing the functional limits of the security blanket relative to the mother. Dev. Psychol. 12 468–469 10.1037/0012-16184.108.40.2068