Can a nametag be placed in a tefillin bag?

There are three categories of sacred objects: kodesh items, tashmishei kedusha (objects that serve the kodesh items), and tashmish d’tashmish (objects that serve tashmishei kedusha). In earlier times, a tefillin bag may have been a tashmish d’kedusha if the tefillin were stored directly inside it. Today’s tefillin are stored in a case which is then kept in a bag, so the bag is now considered a tashmish d’tashmish. Some are stringent and consider the bag a tashmish, since it directly surrounds the retzuos. Those who hold this way should not use the tefillin bag to store other items. Some poskim allow a person to place a name tag in the bag. They explain that the tag is for the sake of the tefillin, allowing them to be returned to their owner in case they are lost or stolen.

Can one use a tallis bag for other purposes?

A tallis is not considered a kodesh item. Therefore, a tallis bag is not in the category of tashmishei kedusha. Other items may therefore be stored in a tallis bag. Although the tallis bag traditionally stores the tefillin bag as well, it does not become sacred because it does not come in direct contact with the tefillin. In cases where it does touch the tefillin, one should be careful not to use it to store mundane items.

Can a case that was used for tefillin be repurposed?

A tefillin case only becomes forbidden for other uses if it was once used for tefillin. If it was not yet used, it may be repurposed even if it had already been designated for tefillin. This concept is known as hazmanah lav milsa (designation is insignificant). However, hazmanah is a necessary component when items that were used to serve kedusha are forbidden for mundane use. Thus, if a case was not designated for tefillin but only happened to be used for storing them,  it does not become forbidden for mundane use.