Justice Rekha Palli also issued notice to Tamil Nadu Chief Minister E K Palaniswami and his deputy O Panneerselvam, to whose group the EC has allotted the 'two-leaves' symbol and sought their stand on the matter.
The court listed the matter for further hearing on February 6.
Dhinakaran's application for using a suitable name and symbol was moved in his main petition challenging the poll panel's November 23, 2017 decision holding the Palaniswami- Panneerselvam faction as the real AIADMK and allotting them the 'two-leaves' symbol.
Senior advocate Kapil Sibal, appearing for Dhinakaran, said a suitable name and symbol was being sought only till the pendency of the main petition, as otherwise the poll panel might declare it as a separate party.
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The EC's lawyer however said the poll panel had nothing to do with the local body elections, when the court asked whether it had any objection to allotting the 'pressure cooker' symbol to Dhinakaran's faction.
The court had left the decision to the Returning Officer who had alloted the 'pressure cooker' symbol to Dhinakaran for the by-poll held on December 21, 2017.
Dhinakaran won the by-poll with a margin of over 40,000 votes from his nearest rival.
The hat symbol was given to the Sasikala-Dhinakaran group by the EC in March 2017 when it had frozen the use of the 'two-leaves' symbol to which the group led by Palaniswami and Panneerselvam had also laid claim.
However, on November 23, 2017, the poll panel had ruled in favour of Palaniswami-Panneerselvam faction by allotting the 'two-leaves' symbol to them for the upcoming by-poll.
The symbol issue has been lingering since April in the aftermath of the announcement of by-poll to Radha Krishnan Nagar Assembly constituency in Tamil Nadu following the death of AIADMK supremo J Jayalalithaa in December 2016.
Earlier, rival factions led by Sasikala and Panneerselvam had staked claim over the symbol. Palaniswami was then in the Sasikala camp. Later, a large number of legislators led by Palaniswami revolted against Sasikala and announced the merger of the two factions.