I have published articles on Brahmin Kshatriya and Vaisya Gotras and a detailed list of Brahmin Gotras.
There have been a lot of queries on Gotras.
Broadly speaking they are of two types.

One informing me that I have left out a Gotra.
As Gotra information is difficult to come by and has to be validated I include the Gotras I missed out provided they stand verification.
There are a lot of Gotras which are not known because Brahmins have dispersed throughout India and have different mother tongues.
I shall be writing on these missed out/rare Gotras shortly after researching into various issues.
The other type of query is as to how one finds his Gotra.
The procedure is as follows.
Find out the Traya Rishis, the three Rishis mentioned in the Pravara.
That is the names of the three/five Rishis in the Abhivadana Mantra,
For example Abhivadaye
Kasyapa Apastara Naithruva
Thraya Rishe
Here the three Rishis are Kasyapa Apastara and Naithruva.
Your Gotra is the one that of the first Rishi
Here it is Kasyapa.
This method is for peoplevwho know Abhivadana but can not name their Gotras(some can not find Gotra even if they know Abhivadana)
For others check from the elders of the family the Sankalpa they perform during pooja orapara kriyas.
From this you can find the three or five Rishis.
If you can not find here or do not know Sankalpa findout the Veda shaka you follow.
If you can not find this find out the names of your paternal grandfather ,great grandfather and let me know the details along with the names of your father,Family Deity and your mother tongue.
I shall try to find out the Gotra.

This is quite interesting. My father and brother used to say till three clans and my husband and son say till the fifth…
Bhargava,shravan,Aplavana,aurva,jamadagna…
My father used to say…
Naithruva,…
Please read my article Gotra Three Five Rishis.Regds
I did not see in your list Srivatsa Gothra – Bhargava, Syavana, Apnavana, Avoorva, Jamadagnia are the 5 rishis.
Please check Brahmin Gotra list article
Our Gothram is Lohita Gothram. Can you please elaborate about this Gothram. I would like to know our Rishi.
Regards.
Kausika viswmitra Agamarshana are the three rishis.
Lohitha Gothram
Pravara : Kowshika, Viswamitra, Aghamarshana, Trayarsheya Pravarnvita, Lohita Gothra Aswalayanasutra, Rikh Shakhadhayayee.
Original Ancestors Of the 74 seats established for the spread of the doctrine by Sri Ramanuja two were headed by brothers, Maruthi Periyandan, and Maronrilla Maruthi Chiriyandan. Of these the first was looking after the private services of Sri Ramanuja and the second was looking after the Mutt administration. When Sri Ramanuja came over to Hoysala Karnataka under the pretext of Chola King persecutions, many came with Sri Ramanuja. At that time, Maruthichiriandan was also with Sri Ramanuja and looking after his private and other secular affairs. In course of time, Sri Ramanuja sent Maruthichiriyandan to Srirangam to bring news of the welfare Kurathalwan and others and about the political situation there at the time. He brought information on all these matters and informed Sri Ramanuja when he was at the Kalyani Tank that the Chola King had died.
i am from Thirunelveli Saiva Pillai caste. How to find out my Gotra?
Shiva Gotra.
I have been trying to trace the origin of my gotra since a very long time but with no success. My gotra is: Shankas. We are Sam Ved Brahmins, Shaiva, Kauthuma Shakha, Tree Pravar. Trivedi.
If you are following Gauthama Shaka you Gotra is Gauthama.
Name-Abhinandan Varur
Father name-Prakash Varur
Mother Name-Sunita Varur
Grand father-Shrikant Varur
Great Grand Father- AppaRao Varur
Grand mothers name- Sarojanni Varur
Grand mothers father- YasvantRao Ankale.
Forefathers occupational -landloards “Savukars”.
Language – Marathi,Kannada.
Place- karnataka,maharastra.
Family Deity?