visual foxpro capacities:(from https://msdn.microsoft.com/en-us/library/3kfd3hw9(v=vs.80).aspx)
Maximum number of characters in field names in a free table 10
Maximum number of characters in field names in a table contained in a database 128

A suggestion (i am not tables oriented !) :
when you create a cursor its have readonly.attribute then you cannot change anything otherwise adding records....
its like a free table and max.field chars cannot up 10 by limitation(troncated).
if you use the select statement and Readwrite option maybe this can solve your problem.

select.........INTO CURSOR ycurs readwrite

try this code

Sele * From Home(1)+"samples\data\customer" Into Cursor ycurs readwrite
brow
ALTER TABLE ycurs RENAME fax  TO azertyD123456789f
brow

see the field FAX how its renamed (without any message error).

*update: modi stru of ycurs cursor(17 chars)
field azertyd123456789f c24