Her grandparents prefer that her name begins with the letter "T" or "R", like her birth sign.
Her grandparents would prefer that her name begin with the letter "T" or "R", like her birth sign.
Her grandparents want her name to begin with the letter "T" or "R", like her birth sign.
Note:I presume you do mean 'birth sign' (some aspect of Indian cullture) and not the astrological sun sign, usually referred to as one's star sign - gemini, virgo etc, since there is no star sign beginning with "R" - the only choice is "T" as in taurus.