As mention in the previous answers, the maximum length of of the field names is not linked with the software but with the format of your file. It seems that your feature class is store in a format that is not a shapefile, and that its file names are truncated when it is exported.
With shapefile (dbase table), the limit is 10 characters
With file and personnal geodatabase, the limit is 64 characters (see here) assuming ANSI text character.
In a native PostGIS database, it is also 64.
With KML, there is (in theory) no limitation
With enterprise geodatabase (assuming ANSI text character), the limit is 30 (Oracle) or 31(others) depending of the underlying RDBMS (see here for details)
note that (from ArcGIS help)
Database management systems have different definitions of acceptable
characters for object names. Most must begin with a letter and cannot
contain spaces or back slashes. Some allow special characters such as
forward slashes (/), underscores (_), dollar signs ($), dashes (-),
dots (.), or mixed cases. Sometimes, the DBMS allows you to use
special characters or force mixed, upper-, or lowercase names if you
provide the object name enclosed in double quotation marks. However,
do not create any tables, feature classes, databases, users, roles, or
other object names using double quotation marks if you will be using
it with ArcGIS; the object will be created in the database exactly as
typed, but ArcGIS will not recognize it, which means you will not be
able to access it from ArcGIS.