ungal peyar enna? 

உங்கள் பெயர் என்ன?

Ungal Paeyar Enna? It's more formal

To younger-Un paeru enna?-Informal

To Older-Unga Paeru enna?-Informal

What-Enna?, Paeyar-Name, Ungal-Yours, Un-You, Unga-You...

unga pearu enna? is correct spoken form.

"peyar" is written form.

pearu actually means person, but in this context it means name.

If you wanted to be more polite you can ask "unga pearu ennanga?" less polite form would be "un pearu enna" - least polite form (intimate) for male is un pearu ennada and female is un pearu ennadi.

Finally words like "amma" "appa" can be appended to "enna" like ennamma and ennappa as a term of respectful endearment to other women and men.

ungaltuia peyar enna?