(Reuters) - Morgan Stanley's wealth management unit will eventually be renamed Morgan Stanley Wealth Management, the investment bank's chief executive said on Tuesday.

A name change for the unit, now called Morgan Stanley Smith Barney, has been rumored for some time. Morgan Stanley Chief Executive James Gorman publicly mentioned the change for the first time during a presentation at a conference.

Morgan Stanley is in the process of buying the Smith Barney business from Citigroup Inc over a period of years. The unit now runs as a joint venture, but will eventually be owned entirely by Morgan Stanley, according to the plan.

(Reporting By Lauren Tara LaCapra; editing by John Wallace)