You could create a couple of temporary helper columns to combine the names in each row and then sort on helper columns.
Example:
<br /><table cellpadding="2.5px" rules="all" style=";background-color: #FFFFFF;border: 1px solid;border-collapse: collapse; border-color: #A6AAB6"><colgroup><col width="25px" style="background-color: #E0E0F0" /><col /><col /><col /><col /><col /></colgroup><thead><tr style=" background-color: #E0E0F0;text-align: center;color: #161120"><th></th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th></tr></thead><tbody><tr ><td style="color: #161120;text-align: center;">1</td><td style="font-weight: bold;;">Last name</td><td style="font-weight: bold;;">First Name</td><td style="font-weight: bold;;">Data</td><td style="font-weight: bold;;">Helper column 1</td><td style="font-weight: bold;;">Helper column 2</td></tr><tr ><td style="color: #161120;text-align: center;">2</td><td style=";">Smith</td><td style=";">Joe</td><td style="text-align: right;;">34</td><td style="text-align: center;;">SmithJoe</td><td style="text-align: center;;">SmithJoe2</td></tr><tr ><td style="color: #161120;text-align: center;">3</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">44</td><td style="text-align: center;;">SmithJoe</td><td style="text-align: center;;">SmithJoe3</td></tr><tr ><td style="color: #161120;text-align: center;">4</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: center;;">SmithJoe</td><td style="text-align: center;;">SmithJoe4</td></tr><tr ><td style="color: #161120;text-align: center;">5</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">55</td><td style="text-align: center;;">SmithJoe</td><td style="text-align: center;;">SmithJoe5</td></tr><tr ><td style="color: #161120;text-align: center;">6</td><td style=";">Jones</td><td style=";">Jim</td><td style="text-align: right;;">22</td><td style="text-align: center;;">JonesJim</td><td style="text-align: center;;">JonesJim6</td></tr><tr ><td style="color: #161120;text-align: center;">7</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: center;;">JonesJim</td><td style="text-align: center;;">JonesJim7</td></tr><tr ><td style="color: #161120;text-align: center;">8</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">33</td><td style="text-align: center;;">JonesJim</td><td style="text-align: center;;">JonesJim8</td></tr><tr ><td style="color: #161120;text-align: center;">9</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">34</td><td style="text-align: center;;">JonesJim</td><td style="text-align: center;;">JonesJim9</td></tr><tr ><td style="color: #161120;text-align: center;">10</td><td style=";">Doe</td><td style=";">Jane</td><td style="text-align: right;;">100</td><td style="text-align: center;;">DoeJane</td><td style="text-align: center;;">DoeJane10</td></tr><tr ><td style="color: #161120;text-align: center;">11</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">50</td><td style="text-align: center;;">DoeJane</td><td style="text-align: center;;">DoeJane11</td></tr><tr ><td style="color: #161120;text-align: center;">12</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">22</td><td style="text-align: center;;">DoeJane</td><td style="text-align: center;;">DoeJane12</td></tr><tr ><td style="color: #161120;text-align: center;">13</td><td style="text-align: right;;"></td><td style="text-align: right;;"></td><td style="text-align: right;;">23</td><td style="text-align: center;;">DoeJane</td><td style="text-align: center;;">DoeJane13</td></tr></tbody></table><br /><br /><table cellpadding="2.5px" rules="all" style=";border: 2px solid black;border-collapse:collapse;padding: 0.4em;background-color: #FFFFFF" ><tr><td style="padding:6px" ><b>Worksheet Formulas</b><table cellpadding="2.5px" width="100%" rules="all" style="border: 1px solid;text-align:center;background-color: #FFFFFF;border-collapse: collapse; border-color: #A6AAB6"><thead><tr style=" background-color: #E0E0F0;color: #161120"><th width="10px">Cell</th><th style="text-align:left;padding-left:5px;">Formula</th></tr></thead><tbody><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">D2</th><td style="text-align:left">=IF(<font color="Blue">A2<>"",A2&B2,D1</font>)</td></tr><tr><th width="10px" style=" background-color: #E0E0F0;color: #161120">E2</th><td style="text-align:left">=D2&ROW(<font color="Blue"></font>)</td></tr></tbody></table></td></tr></table><br />
The two helper columns (D and E in this case) can be any empty columns.
The formula in D2 combines the Last and First names . If the Names don't exist in the row then the combined names from the previous row is used. Copy the formula in D2 down column D.
The formula in E2 numbers each of the combined names in column D. This is so the rows for a given name are not sorted. Copy the formula in E2 down column E.
Before you sort on Column E, you want to convert the formulas into values so the values don't change during the sort. Select column E and copy. Select from the menu...
Edit \ Paste Special: Values
You should now be able to sort on column E and all the data for a given name should stay grouped together. You could delete the helper columns after the sort.