London Welsh chairman Bleddyn Phillips says the club may consider rebranding in an attempt to connect to their Oxfordshire base, but is also eager not to eradicate 130 years of tradition.
They moved to Oxford from Richmond last year after reaching the Premiership.
Welsh stayed in the county following relegation, but crowds have been poor.
"The challenge for us as a club is to make sure we come up with an identity the people of Oxfordshire feel a part of," Phillips told BBC Oxford.
Welsh are unbeaten this season as they look to return to the Premiership at the first attempt, but have failed to attract the crowds of 3,000-4,000 they hoped for, with just 1,200 attending the victory over Cornish Pirates.
Vice-chairman Kelvin Bryon released a statement last month stating his disappointment at attendances and Phillips said they were open to any ideas of how the club can "establish an identity with Oxfordshire", without turning their back on their history.
"London Welsh as a world-recognised brand name is very important," he continued.
"I would just like to think that we would have to consider very carefully making any change to the words London Welsh without bearing in mind the consequences of doing so. Equally, we have to be mindful of the fact we are playing in Oxford.
"The big question is, how do we marry the two together? I would welcome ideas of how we address the problem. I think there is an answer, what it is, I do not know."
Phillips shares Bryon's disappointment at the size of home crowds this season, but conceded it will take time to build up a loyal following in the county.
He said any decision to rebrand or rename would not be taken overnight and would be done with a heavy heart.
"Identity is critical. London Welsh as a name has been going for almost 130 years and I think we would just jettison our name and all London Welsh stands for and the history and tradition at our peril," he added.
"I think it would be a mistake to lose that brand name - heritage is terribly important. Having said that if we are going to move to Oxford on a long-term basis, then we need to associate with Oxfordshire a lot more closely as well.
"The challenge in the short to medium term is going to be to galvanise both the fact we are playing in the Oxfordshire area and yet not lose that tradition and brand name of London Welsh that has been so important for so long."