If SuSE SLES12 has mcp/mmv command in its repository, then it would be simple use of mmv:
mmv 't_*.png' '#1_t.png'
Or, if the number of characters and specific numbers was issue, you could be more specific like:
mmv 't_00??_000???.png' '00#1#2_000#3#4#5_t.png'
First argument to mmv is source, with standard wildcards * and ?. The second argument is destination, in which #1 is replaced with content which first wildcard matched, #2 with content which second wildcard matched etc.
Example:
% ls -1
t_0011_000037.png
t_0011_000038.png
t_0011_000039.png
t_0022_000001.png
t_0022_000002.png
% mmv 't_*.png' '#1_t.png'
% ls -1
0011_000037_t.png
0011_000038_t.png
0011_000039_t.png
0022_000001_t.png
0022_000002_t.png
prenameand no admin rights to install anything.t_*, I can usemvcommand, something likemv t_* *_twhere * is a single filename within the loopmvdoesn't work like that. It's going to take*_tas a directory name then give you an error when it doesn't exist.