All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It appears that the name 'Alliyah does not have a bad meaning therefore there is no harm to have such a name, Inshaa' Allaah. Moreover, you are not obliged to change your name in official documents unless you fear the loss of some rights by not doing so. As regards your family, you have no right in principle to oblige them to call you 'Alliyah, but if you can convince them, then that is good. However, if you fear that if you discuss this matter with them there would be some embarrassment, then it is more appropriate to avoid discussing it. Finally, if should be noted that if a name does not include a meaning that is objectionable in Islam then one is not obliged to change it; on this matter please refer to Fataawa: 84551 and 86211.
Allaah knows best.