Yes, Excel will run out of table names. As Jules notes (and can be confirmed by trying long names in Excel), Excel table names are limited to 255 characters (as of the time of writing- I'm using Excel 2010). So, there is a finite number of table names available.
However, the number of possibilities is very, very high. It is not quite every combination of letters and numbers up to a 255 character string since some combinations are not allowed, such as names that could also be a cell reference (the table name "T100" is not allowed as it could also mean cell T100).
Assuming that you continue naming tables from "Table1" to "TableN":
Your largest table name would be
Table9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
If you added 100 Billion tables every second, you could add tables for
1,157,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407,407
days.
According to Sydney Observatory, the Earth will be engulfed by the Sun long before you ever run out of table names.
Feel free to check my math- correct me if I've made a mistake:
9,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999
/ (100,000,000,000 * 60 * 60 * 24)