Capital Gain Tax

If the property sold is residential house property then she can claim exemption of capital gains from income tax ,if she complies sec 54 .
sec 54 says if any individual invests the capital gain from transfer of residential house property and land appartuenent therto in any other residential property with in 2 years for acquisition and 3 years for construction,then entire capital gains shall be Exempted.
This section is amended recently and from FY2019-20, investment can be made in 2 Residential properties with in the above time lines.But this option is available only once for the assessee over his lifetime.so you can invest in upto residential houses .
With respect to name ,you can invest in either of your family names