According to Final Fantasy Name Origins: Goes back to a family of hereditary regents to the shogunate of Japan who exercised actual rule from 1199 to 1333. During that period, nine successive members of the family held the regency. The Hojo took their name from their small estate in the Kanogawa Valley in Izu Province. Hojo = power. There may be a more subtle meaning to this, but I fail to see it.
Unlike most of the names in Final Fantasy 7, Hojo's is not written in katakana. "Hojo" is written with two kanji. The first character means "treasure". The second means "reason". This ties in closely with Hojo's love for and dependance on science. One of the most important qualities in a scientist is logic or reason, and so Hojo's reason is his most valuable treasure.
(Randomly enough, a completely different kanji combination that also is pronounced "hojo" means fertility. I wonder if this is a pun Japanese players would have caught in reference to Sephiroth's creation?)
As for the Hojo clan itself, the Grolier Encyclopedia states that during the Kamakura Period in Japanese history, the Hojo clan wrested control of the shogunate and actual power in Japan, while the emperor remained a mere figurehead. This is rather similar to Professor Hojo's position at Shinra - he remains ostensibly under the control of the emperor (President Shinra) but is the one actually ruling the country (plot of the game) and could not be stopped by the emperor's forces if he chose to move against him.
An interesting note:
An example of the continuing power of women in the early feudal period is Hojo Masa-ko. This strong-willed woman seized the reins of the shogunate after her husband, the first shogun Yoritomo Minamoto, died in 1199. She quickly maneuvered her own family, the Hojo clan, into a regency over her son Yoriie. In her old age it was she who galvanized the shogunate army which crushed the forces of the Emperor Go-Toba in 1221. The Hojos remained as regents over all the successive Minamoto shoguns for the next century and a half. For this reason Hojo Masa-ko, known as "Mother Shogun," has been referred to as the founder of the shogunate. - Samurai Sisters: Early Feudal Japan