A private company must end in either of these – it doesn’t matter which one that you use, it is matter for you to decide. You can choose to amend this after incorporation but it would be better to decide before hand and save the expense of a name change.
If you are a private limited company by guarantee, you may be able to apply for an exemption from using limited or Ltd. Your articles of association must state that the objects of the company are for the promotion of commerce, art, science, education, religion, charity or profession incidental or inductive to these objects, also prohibit the payment of dividends or the return of capital to members and all assets upon the company winding up be transferred to another body or company with similar objects. (You can apply for an exemption on section A3 of the IN01 application)