Change name on land registry

My mum passed away 3 years ago, the family home was joint owned with my father as tenants in common. Mums 50% was left to my sister and I in her will with dad to remain living in the property. We never applied for grant of probate following mums death. As the land registry is in mum and dad’s name do we need to change the name to include me and my sister or just remove mums name ?

Tracey - that's a decision only you and your Father/sister can make. We register the outcome of any decision made and can't advise you on what you should or is 'best' to do.
The legal ownership has passed to your Father to deal with so if you all decide the property is to be transferred then he would transfer the whole of the title to whoever.
The TIC/50% share relates to their beneficial ownerships and that's usually defined in their wills/trust deed as appropriate. Such an arrangement is often protected on the register by what's known as a form A/joint ownership restriction although it doesn't have to be. Joint property ownership: Overview - GOV.UK 
I would therefore recommend discussing your options with a legal rep before deciding whether to transfer the legal ownership/update the register.
Once you have decided what you want to do our online assisted guidance explains how to apply to us to then update the register as appropriate - HMLR Guide: Start - External  · HM Land Registry