Yes, its usually called Internalised homophobia.
Internalized homophobia (or ego-dystonic homophobia) refers to homophobia as a prejudice carried by individuals against homosexual manifestations in themselves and others. It causes severe discomfort with or disapproval of one's own sexual orientation. The label of internalized homophobia is sometimes applied to conscious or unconscious behaviors which an observer feels the need to promote or conform to the expectations of heteronormativity or heterosexism. This might include making assumptions about the gender of a person's romantic partner, or about gender roles. Some also apply this label to LGBT persons who support "compromise" policies, such as those that find civil unions an acceptable alternative to same-sex marriage.
Homophobia is defined as the "unreasoning fear of or antipathy toward homosexuals and homosexuality." It operates on two levels: internally and externally. Internal homophobia represents prejudices that individuals incorporate into their belief systems as they grow up in societies biased against gays and lesbians. External homophobia is the overt expression of those biases, ranging from social avoidance to legal and religious proscription to violence.
TO A LARGE EXTENT, American society has made gay men and lesbians the brunt of multiple levels of prejudice, with negative assumptions about their morality, trustworthiness, employability, and integrity. (Similar accusations have been made against African-Americans, Jews, and other
ethnic groups.) As a result, gay men and lesbians developed a hidden subculture among themselves that only recently has become much more open, and now weaves throughout all segments of society.