Hi Vishwanatha,
If you check the table BUT000, you will see the corresponding text fields for name 1 and name 2( or first name and last ) as MC_NAME1, MC_NAME2. These are the fields which makes the searching with any case even it's lower case or upper case. But if you check the domain of field First name which is BU_NAME, it allows lower case. But for MC_NAME1 it won't allow and it stores the data as upper case only always.You can take some examples and see.
In order to make your field search relevant in all cases is, create one more field where the same value of your field will be saved with upper case. While searching, use this field to compare. Issue will be resolved.
Thanks,
Faisal