RBS is a stand-out performer in the UK in the 2013 Banking 500 survey published by The Banker magazine and conducted by global brand valuation consultancy Brand Finance.
The rise in the value of the RBS brand over the past 12 months contrasts with sharp falls for HSBC and Standard Chartered and a modest decline for Barclays.
Lloyds Banking Group's Bank of Scotland unit has achieved a slight increase in its brand value, to $1.884bn (£1.19bn) in the 2013 survey from $1.802bn a year ago, while its Scottish Widows operation has enjoyed a jump from $1.158bn to $1.346bn.
Edinburgh-based RBS has now enjoyed four consecutive years of increase in the value of its brand, according to the survey. The value of the RBS brand had plunged from $6.117bn in early 2008 to $2.584bn at the start of 2009.
RBS came close to collapse in the autumn of 2008, under previous chief executive Fred Goodwin, and required an injection of tens of billions of pounds of taxpayer funds.
Mr Goodwin was succeeded by Stephen Hester, who has been chief executive of RBS since November 2008.
Bank of Scotland's brand value had been put at $3.024bn in early 2008. Its parent group, HBOS, also had to be bailed out by the taxpayer in autumn 2008 and was the subject of a rescue takeover by Lloyds TSB, a deal which formed Lloyds Banking Group.
By early 2009, Bank of Scotland's brand value was calculated to have tumbled to $1.075bn. It had risen slightly to $1.183bn by early 2010, and had climbed to $1.893bn by the start of 2011.
Brand Finance and The Banker point out their survey shows that the UK is the only top 10 country to have seen the total value of its bank brands fall in the latest year.
The total value of UK bank brands has dropped by $1.5bn in the last year, from $68bn to $66.5bn, on the basis of Brand Finance's calculations.
According to the survey, the value of HSBC's brand has fallen from $27.6bn to $22.9bn.
The Banker and Brand Finance highlight HSBC's fall from first to third position in the global rankings and declare this brand has been "hit by money-laundering allegations" and affected by the divestment of several major investments which have resulted in lost revenues.
US bank Wells Fargo has taken global top slot in the study as a result of a rise in its brand value from $23.2bn to $26bn. Fellow US bank Chase is second, having seen its brand value rise from $19bn to $23.4bn.
Those behind the study meanwhile highlight the impact of money-laundering allegations on UK-based Standard Chartered, with the value of this brand calculated to have dropped from $7.624bn to $7.022bn.
And they note Barclays' part in the Libor rate-fixing scandal. Barclays' brand value is calculated to have dipped from $13.552bn to $13.436bn.
Brand Finance chief executive David Haigh said: "UK banks seem to be accident-prone. Last year's leading UK bank brands have defied the global trend by going backwards. The laggards of 2009 are finally recovering but the reputation of the UK banking industry has been seriously damaged."
The survey shows that strong growth in emerging economies has helped drive a 15% rise in total bank brand values to $860.7bn from $746.8bn a year ago. It highlights strong growth in recent years in the values of banks in Russia, Indonesia, the Philippines, Colombia, and China, declaring: "The presence and might of the Chinese banks has been ever-growing."