When a mesh partitioning takes place and every process works on a part of the mesh is any way to rename the global numbering of nodes(on each process) into a local numbering?Is there any software that can do it?
All software I know of first enumerates nodes locally, and then uses this local enumeration to generate a global enumeration.
I suggest that you want to read the following manuscript about all of these questions: https://www.math.colostate.edu/~bangerth/publications/2010-distributed.pdf In particular, section 3 is relevant to you. The full reference for this paper is as follows:
Wolfgang Bangerth, Carsten Burstedde, Timo Heister, Martin Kronbichler: "Algorithms and data structures for massively parallel generic adaptive finite element codes". ACM Transactions on Mathematical Software, vol. 38 (2011), pp. 14/1-28.