The names of places where archaeological excavations were done also sound as Tamil.
To name a few taken from this website
Kääpa - kaappu (protection)
Narva Joaoru - naravu (toddy, milk)
Riigiküla - kulam (lineage)
Siimusaare - siimam (boundary)
Tamula - Tamil?? (Tamila)
Pulli - Pulli (petal, dot)
Valma - valimai (strength)
Update added on 25th June 2017:-
I happened to read about the practice of naming children as "Pulli" in Telugu speaking community that once lived in north of Madras. The source of this is "Indian Antiquary", volume 10, published in the year 1881.
The practice until the 19th century was to name the child born after the death of its older sibling, as Pulli. For boys, the name is "Pulya" and for girls the name is "Pullama"
Pulli-akalu is a leaf that was used as a plate for eating food in those days. These are thrown out on a heap and when the child is born (after the death of the elder child), two or three of them are brought and placed on the child.
Naming the child as "Pulli" had another explanation among the people of those times. Pulli means hole. (In Tamil it means dot. The Kolam are made around the dots / pulli). The previous child is dead leaving a hole, and the new child has come to fill up the hole. Based on this rationale, the new child was named Pulli.
It would be interesting to know the kind of customs that Pulli people of Estonia followed.